The angle of elevation to the top of a 20-story skyscraper is measured to be 10 from a point on the ground 1,500 feet from the building. Find the height of the skyscraper in feet, correct to three decimal places.

(Points : 5)
260.47

73.86

972.54

264.49 <--

Let f(x) = sin-1x. Then the domain of f(x) is [-1,1] and the range is all real numbers.
(Points : 5)
True

False <--

first question is correct

#2 should be true.
sin^-1 (x) means find the angle Ø so that sinØ = x
since the result of taking the sine is always a number between -1 and +1
then for sin^-2 (x) , your choice of x has to be -1 ≤ x ≤ 1

e.g try taking sin^-1 (1.4) on your calculator
that is
2nd
sin
1.4
=

you should get an "error" result

Thank you so much!

To find the height of the skyscraper, we can use trigonometry and the concept of similar triangles.

First, let's draw a diagram to visualize the problem.

- Ground
|
|\
| \
| \
| \
| \
A |-------\-------------------- B
| \
|h \
| \
|θ \
| \
|____________\
Skyscraper

In the diagram above, A represents the point on the ground where the angle of elevation is measured, B represents the top of the skyscraper, h represents the height of the skyscraper, and θ represents the angle of elevation.

The given information tells us that the angle of elevation is 10 degrees and the distance from point A on the ground to the skyscraper (point B) is 1,500 feet.

Using trigonometry, we have the following relationship for the tangent of an angle:

tan(θ) = opposite/adjacent

In this case, the opposite side is the height of the skyscraper (h) and the adjacent side is the distance from point A to point B, which is 1,500 feet. So we can rewrite the equation as:

tan(10) = h/1500

To find the height h, we can multiply both sides of the equation by 1500:

1500 * tan(10) = h

Calculating the value on the left side gives us:

1500 * tan(10) ≈ 261.47

Therefore, the height of the skyscraper is approximately 261.47 feet.

So the correct answer from the given options is 264.49.