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.

A bug is shown on level ground a distance of x to the left of the base of a statue.

(1 point)
The bug is
feet from the statue.

Answer 1

To find the distance from the bug to the statue, we can use the tangent function from trigonometry. The bug's sightline to the top of the statue creates a right triangle where:

- The height of the statue (opposite side) is 13 feet.
- The angle of elevation to the top of the statue is 35 degrees.
- The distance from the bug to the statue (adjacent side) is what we are trying to find.

Using the tangent function:

\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\]

Substituting in our known values:

\[
\tan(35°) = \frac{13}{x}
\]

Where \(x\) is the distance from the bug to the statue. Rearranging the equation to solve for \(x\):

\[
x = \frac{13}{\tan(35°)}
\]

Now we will calculate \(\tan(35°)\) and then find \(x\):

1. Calculate \(\tan(35°)\):
\(\tan(35°) \approx 0.7002\)

2. Now, substitute this back into the equation for \(x\):

\[
x = \frac{13}{0.7002} \approx 18.5587
\]

Rounding \(x\) to the nearest tenth of a foot gives:

\[
x \approx 18.6
\]

Therefore, the bug is **18.6 feet** from the statue.