Question

A building casts a shadow reaching 13 feet from the base of the building, with a diagonal distance of 15 feet from the top of the building. Using the inverse of sine, what is the approximate angle formed between the top of the building and the shadow?(1 point)
Responses

90°
90°

60°
60°

45°
45°

30°

Answer 1

To find the angle formed between the top of the building and the shadow, we can use the sine function.

In a right triangle formed by the building, the shadow, and the line from the top of the building to the tip of the shadow:

- The opposite side is the height of the building (let's call it \(h\)).
- The adjacent side is the length of the shadow, which is 13 feet.
- The hypotenuse is the diagonal distance from the top of the building to the tip of the shadow, which is 15 feet.

We need to find the angle \(\theta\) such that:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{15}
\]

We also know that the length of the shadow (adjacent side) is 13 feet. Using the Pythagorean theorem:

\[
h^2 + 13^2 = 15^2
\]

\[
h^2 + 169 = 225
\]

\[
h^2 = 225 - 169 = 56
\]

\[
h = \sqrt{56} \approx 7.48 \text{ feet}
\]

Now we can calculate \(\sin(\theta)\):

\[
\sin(\theta) = \frac{7.48}{15} \approx 0.4987
\]

Now, to find the angle \(\theta\):

\[
\theta = \sin^{-1}(0.4987) \approx 29.9°
\]

Therefore, the approximate angle formed between the top of the building and the shadow is 30°.

The correct answer from the choices given is **30°**.