Question

A bug on Easter Island stands on level ground by a Moai statue. The statue is 13 feet tall. The bug’s sightline to the top of the statue makes an angle of 35°. How far away from the statue is the bug? Round your answer to the nearest tenth of a foot.

Answer 1

To find the distance from the bug to the base of the Moai statue, we can use the tangent function from trigonometry. The tangent of an angle in a right triangle is defined as the opposite side divided by the adjacent side.

In this scenario:
- The height of the statue (the opposite side of the triangle) is \( 13 \) feet.
- The angle of elevation from the bug's sightline to the top of the statue is \( 35^\circ \).
- We need to find the distance from the bug to the base of the statue (the adjacent side of the triangle).

Using the tangent function:

\[
\tan(35^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{13}{d}
\]

where \( d \) is the distance from the bug to the statue. Rearranging the equation, we get:

\[
d = \frac{13}{\tan(35^\circ)}
\]

Now, we need to calculate \( \tan(35^\circ) \). Using a calculator, we find:

\[
\tan(35^\circ) \approx 0.7002
\]

Now, substituting this back into our equation for \( d \):

\[
d = \frac{13}{0.7002} \approx 18.55
\]

Rounding to the nearest tenth, we find:

\[
d \approx 18.6 \text{ feet}
\]

Thus, the distance from the bug to the Moai statue is approximately \( \boxed{18.6} \) feet.