an observer is 120 feet from the base of a television tower that is 140 ft tall. Find to the nearest degree the angle of elevation of the top of the tower from the point where the observer is standing
Answers
The angle of elevation is obtained as follows:
Step 1: Make a sketch of the scenario, as below?
Step 2: Apply the appropriate trigonometric ratio to obtain the unknown angle, as follows:
\(\text{tan}\theta=\frac{opposite}{adjacent}\)With respect to the unknown angle:
opposite = 140 ft
adjacent = 120 ft
Therefore:
\(\begin{gathered} \text{tan}\theta=\frac{opposite}{adjacent} \\ \Rightarrow\text{tan}\theta=\frac{140\text{ ft}}{120\text{ ft}}=\frac{140}{120}=1.1667 \\ \Rightarrow\text{tan}\theta=1.1667 \\ \Rightarrow\theta=\tan ^{-1}(1.1667)=49.4^o \\ \Rightarrow\theta=49^o\text{ (to the nearest degre}e\text{)} \end{gathered}\)Therefore, the angle of elevation is 49 degrees
Related Questions
Warm Up
1. Find the distance between points at
(10, 7) and (-4, 8).
Answers
Or
1 unit up, 14 units left
The prices of houses in the US are strongly skewed to the right with a mean of $383,500 and a standard deviation of $289,321. A real estate agent takes a random sample of 10 houses and records the mean price. What is the shape of the distribution of the sample mean for all possible random samples of size 10 from this population?
Answers
Answer:
strongly skewed right
Step-by-step explanation:
since the sample size is under 30, it will remain skewed right.
The shape of the distribution of the sample mean for all possible random samples of size 10 from this population is strongly skewed right.
What is sampling?It should be noted that sampling simply means the selection process from a particular population.
In this case, the shape of the distribution of the sample mean for all possible random samples of size 10 from this population is strongly skewed right. This is because the sample size is under 30.
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Vector u has initial point P at (0, 0) and terminal point Q at (4, −7). What are the component form and magnitude of u?
Answers
Answer:
u=(4,-7);||u|| sqrt 65
Step-by-step explanation:
65 cant be negative.
U is the same as Q since P is 0,0
Why might young adults,in particular,value credit in case of emergency
Answers
Young adults might value credit in case of an emergency for several reasons. Firstly, credit provides financial flexibility, allowing them to access funds quickly when unexpected expenses arise.
This can be essential for covering costs related to medical emergencies, car repairs, or other unforeseen events that may strain their limited savings. Secondly, young adults often have less established financial safety nets than older individuals. They may not have significant savings, insurance policies, or support from family members to fall back on during emergencies. Credit, in this case, acts as a temporary financial cushion, enabling them to manage immediate needs without resorting to high-interest loans or further jeopardizing their financial stability.
Thirdly, responsible use of credit can help young adults build a positive credit history. Demonstrating responsible borrowing and repayment habits will make it easier for them to access more favorable credit terms in the future, such as lower interest rates or higher credit limits. This can prove valuable when making significant purchases, like buying a home or financing higher education.
Lastly, having access to credit can also provide young adults with a sense of financial independence and empowerment. Knowing they have the means to handle emergencies without relying on others can boost their confidence in managing personal finances and help them make more informed financial decisions as they navigate adulthood.
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After watching baking shows on T.V., Angie signs up for a cake-decorating class. To practice her new skills, she decorates a batch of cupcakes with sugar flowers. Angie puts 4 sugar flowers on each cupcake. In all, Angie puts 32 sugar flowers on the cupcakes.
Which equation can you use to find the number of cupcakes c Angie decorates?
Solve this equation for c to find the number of cupcakes Angie decorates.
Answers
Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.
To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.
4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.
To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8
Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8
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Jessica needs to rent a moving truck for one day. She can choose to rent a moving truck from Rentals Plus or from Speedy Move. At Rentals Plus, it costs $5.24 to rent a moving truck for one day, plus $4.46 per mile driven. At Speedy Move, it costs $85.24 to rent a moving truck for one day, plus $0.46 per mile driven. How many miles would Jessica have to drive for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move?
Answers
Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.
How find how many miles would Jessica have to driveLet's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:
Cost at Rentals Plus = $5.24 + $4.46 * m
Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:
Cost at Speedy Move = $85.24 + $0.46 * m
To find the number of miles that makes the costs equal, we can set up the equation:
$5.24 + $4.46 * m = $85.24 + $0.46 * m
By rearranging the equation, we can solve for 'm':
$4.46 * m - $0.46 * m = $85.24 - $5.24
$4 * m = $80
m = $80 / $4
m = 20
Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.
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What is the value of q?
a. 4√5
b. 2√14
c. 20√5
d. 64√5
Answers
9514 1404 393
Answer:
(b) 2√14
Step-by-step explanation:
The geometric mean theorems applicable to this geometry are ...
q = √(4·(4+10))
q = 2√14
__
Other unknowns
r = √(10·(10+4)) = 2√35
s = √(10·4) = 2√10
What are three consecutive multiples of 3 if 2/3
of the sum of the first
two numbers is 1 greater than the third number?
Answers
The three consecutive multiples of 3 are 15, 18 and 21
To solve this problem
First, let's determine three successive multiples of 3:
The subsequent two would be "x+3" and "x+6" if we call the initial number "x".
Since we are aware that the third number (x+6) is one more than the first two numbers (x + x+3), we can write the following equation:
2/3(x + x+3) = (x+6) + 1
Simplifying this equation, we get:
2/3(2x+3) = x+7
Multiplying both sides by 3, we get:
2(2x+3) = 3(x+7)
Expanding and simplifying, we get:
4x + 6 = 3x + 21
Subtracting 3x and 6 from both sides, we get:
x = 15
Therefore, the three consecutive multiples of 3 are 15, 18 and 21
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Pls help me with math ASAP
Answers
This means their angles add up to 180° which is a straight line
Answer:
Its c
Step-by-step explanation:
B (-1,6) and d (9,4) midpoint formula
Answers
We have two points and we have to calculate the midpoint.
The coordinates of the midpoint are the average of the coordinates of the two points.
In this case, we have B=(-1, 6) and D=(9, 4), so we can calculate the coordinates of the midpoint M as:
\(x=\frac{x_B+x_D}{2}=\frac{-1+9}{2}=\frac{8}{2}=4\)\(y=\frac{y_B+y_D}{2}=\frac{6+4}{2}=\frac{10}{2}=5\)So the coordinates of the midpoint between B and D is (4, 5).
We can graph it so we can see it:
Give an example of a function with both a removable and a non-removable discontinuity.
Answers
Answer:
(x+5)(x-3) / (x+5)(x+1)
Step-by-step explanation:
A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.
Which statement describes the relationship between x
and y?
As x increases, y decreases.
QAs x increases, y increases.
O As x increases, y increases and then decreases.
As x increases, y decreases and then increases.
Answers
Answer:
1.) inverse proportion : 1kx = y
2) direct proportion. y = kx
An account is opened with an initial deposit of $100 and earns 3.0% interest compounded monthly. What will the account be worth in 25 years? Round your answer to the nearest dollar.
Answers
Answer:
A = $211.50
A = P + I where
P (principal) = $100.00
I (interest) = $111.50
Step-by-step explanation:
$209.37 will the account be worth in 25 years.
What is compound interest?Compound Interest is defined as interest earn on interest.
\(A = P(1 + \frac{r}{100})^{t}\)
P= $100
r = 3%
t=25 years
substitute the values in formula,
\(A = 100(1 + \frac{3}{100})^{25}\)
\(A = 100(1 + 0.03)^{25}\)
\(A = 100(1.03)^{25}\)
\(A=100(2.0937)\)
\(A=209.37\)
Hence, $209.37 will the account be worth in 25 years.
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dana can travel 5 miles in 45 minutes on her bicycle if she travels at a constant speed how long does it take her to travel 3 miles
Answers
Answer: 27 minutes
45 min divided by 5 miles is 9 minutes/mile so 3(9) is 27
Please help me help help me please help help me
Answers
We can consider a complex number as a point on a plane such that a+ib=(a,b).
Furthermore, the distance between two points on a plane is given by the formula below.
\(D=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}\)Therefore, in our case,
\(\begin{gathered} 5=5+i0=(5,0) \\ 4i=0+4i=(0,4) \\ \end{gathered}\)Then,
\(\Rightarrow D=\sqrt[]{(5-0)^2+(0-4)^2}=\sqrt[]{25+16}=\sqrt[]{41}\)Therefore, the answer is sqrt(41). Type in 41
complete the 2 column proof below given j = h and line m bisects gk
Answers
A Gallup poll conducted in November of 2011 asked the following question, “What would you say is the most urgent health problem facing this country at the present time?” The choices were access, cost, obesity, cancer, government interference, or the flu. The responses were access (27%), cost (20%), obesity (14%), cancer (13%), government interference (3%), or the flu (less than 0.5%).
The following is an excerpt from the Survey Methods section. “Results for this Gallup poll are based on telephone interviews conducted Nov. 3-6, 2011, with a random sample of 1,012 adults ages 18 and older, living in all 50 U.S. states and the District of Columbia. For results based on a total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±4 percentage points.”
Answers
The results show that the most common response was access, with 27% of the respondents choosing it as the most urgent health problem.
Cost came in second place, with 20% of the respondents choosing it. Obesity and cancer followed closely behind, with 14% and 13% of the respondents choosing them, respectively. Government interference and the flu were the least common responses, with only 3% and less than 0.5% of the respondents choosing them, respectively.
The margin of sampling error for the poll is ±4 percentage points, which means that if the poll was conducted multiple times, 95% of the time, the results would be within 4 percentage points of the actual population values.
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What is the difference of 620 and 89.7?
Answers
Answer: 530.3
Step-by-step explanation:
Difference means to subtract
620-89.7=530.3
Answer:
530.3
Step-by-step explanation:
You want to subtract 620-89.7. If you want to use the standard algorithm you have 620.0-89.7. You "borrow" from the 2 in the tens place, then "borrow" from the ones place. To subtract 10-3 tenths. Then you subtract the ones place which is 9-9=0 ones. Now you subtract 62-8=53 tens. So you have 530.3 as the difference.
Last year and investor purchased 115 shares of stock A at $90 per share
Answers
The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10
The third option is correct.
How do we calculate?For stock A:High price value: 115 shares * $105.19 per share = $12,084.85
Low price value: 115 shares * $103.25 per share = $11,858.75
For stock B:High price value: 30 shares * $145.18 per share = $4,355.40
Low price value: 30 shares * $143.28 per share = $4,298.40
The overall value at high price:
$12,084.85 + $4,355.40
= $16,440.25
The overall value at low price:
$11,858.75 + $4,298.40
= $16,157.15
In conclusion, the difference in overall gain or loss:
$16,440.25 - $16,157.15 = $280.10
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If you know how to solve this, Please answer it. Thank You
The first one to answer the question right, will get Brainlist!
I PROMISE!!!!!
Answers
y = ( x + 9 )^2 - 2
................................
................................
The radius of a circle is 4 miles. What is the length of a 45° arc?
45°
r=4 mi
Answers
The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.
To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.
Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π
The length of the 45° arc is approximately 3.14 miles.
Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.
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Find the measures of angles a and b and of arc c Please
Answers
The measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.
In the given diagram, we can see that angle ACD is a right angle, since it is formed by the radius AC and tangent CD at point C.
Therefore, angle BCD is equal to angle ACD, which is 90 degrees.
Since angle BCD is an exterior angle of triangle BCF, it is equal to the sum of the two remote interior angles, which are angles BFC and FCB.
Angle BFC is equal to angle ABC (since they are opposite angles), which is 60 degrees.
Similarly, angle FCB is equal to angle ACF, which is also 60 degrees.
Therefore, angle BCD is equal to angle BFC + angle FCB, which is 60 + 60 = 120 degrees.
Now, since arc CD is subtended by angle BCD, its measure is also equal to 120 degrees.
Hence, the measure of arc CD is 120 degrees.
Similarly, angles ACF and FCB are opposite angles in the cyclic quadrilateral AFCB, so they are supplementary. Therefore, angle FCB is equal to 180 - angle ACF,
Which is also 180 - 60 = 120 degrees.
Now we can apply the exterior angle theorem to find the measure of angle BCD. We have:
angle BCD = angle BFC + angle FCB
= 120 + 120
= 240 degrees
Finally, we can conclude that the measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.
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In which quadrant would you find the graph of (-5, -6)?
O AT
O B) ||
O C) IUI
O D) IV
Answers
Answer:
Third quadrant
Step-by-step explanation:
To count quadrants, you do it counter-clockwise, so, since the point is in the (negative, negative) quadrant, it is the third one
[Pic] Name a face of the solid.
![[Pic] Name a face of the solid.](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/B4jcJOhKLITXRuhL4j6dP4ek4BRwtCYd.png)
Answers
Answer:
Option C.
Step-by-step explanation:
Solid in the given picture is a rectangular prism and a rectangular prism has 6 faces. Each face is formed by joining 4 vertices of the prism.
All the faces joining four vertices are: AFGB, BGHC, ADEF, DCHE, FEHG, ADCB.
From the given options,
Option (C). ADEF will be one of the face of the solid.
whats 3/2 divided by 8/3 in fraction form
Answers
Answer:
9/16
Step-by-step explanation:
3/2 / 8/3 =
3/2 x 3/8 = 9/16
Hope that helps!
I WILL MARK BRAINIEST
please answer the one I got wrong
Answers
The base of the model merry-go-round is 450in², and the actual merry-go-round's base is 400 times larger.
Therefore the base of the actual merry-go-round is 180,000in². However, the question asks for the answer in square feet.
180,000in² in squared feet is:
1,250ft² (your final answer)
Mr. Wang and Mrs. Wang have 3 sons. Every son has 1 wife, 1 son, 1 sister. How many people in this family?
Answers
If Mr. Wang and Mrs. Wang have 3 sons and every son has 1 wife, 1 son, and 1 sister, the total number of people in the family, based on mathematical operations, is 14.
How is the total number determined?The total number of people in the family can be determined using the mathematical operations of multiplication and addition.
Multiplication and addition are two of the four basic mathematical operations.
Multiplication involves the multiplicand, the multiplier, and the product, while addition involves two or more addends added to get the sum.
The number of parents = 2
The number of sons = 3
The number of additional family members for each son = 3
The total number of additional family members = 9 (3 x 3)
The total number of persons in the family = 14 (9 + 3 + 2)
Thus, there are 14 people in the family of Mr. Wang and Mrs. Wang.
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The graph of a quadratic function with vertex (0, 3) is shown in the figure below.
Answers
The domain of the function is (-∞, ∞.)
The range of the function is {3, ∞}.
We have,
From the given quadratic function,
We see that,
The x-values are -∞ to ∞
The y-values are from 3 to ∞
Now,
The x-values are called the domain.
The y-values are called the range.
Thus,
The domain of the function is (-∞, ∞.)
The range of the function is {3, ∞}.
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A company is making aid badges with personal ID codes on them for each employee. The ID code will consist of two letters followed by 2 digits. Using this scenario, how many possible ID codes are there?
Answers
Answer:
67, 600
Step-by-step explanation:
There are 26 alphabet and 10 digits then the number of the possible ID codes will be 67600.
What are permutation and combination?A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
A company is making aid badges with personal ID codes on them for each employee.
The ID code will consist of two letters followed by 2 digits.
Then the number of ways ID codes are there will be
\(\rightarrow 26 \times 26\times 10\times 10\\\\\rightarrow 67600\)
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A customer's checking account had $302 when he wrote two checks for $101, and three checks for $71. What is his new balance?
The new balance is
dollars.
Answers
Answer:
$717
Step-by-step explanation:
because I did the math