Question

A boat is heading towards a lighthouse, whose beacon-light is 113 feet

above the water. The boat's crew measures the angle of elevation to the
beacon, 11°. What is the ship's horizontal distance from the lighthouse
(and the shore)? Round your answer to the nearest tenth of a foot if
necessary.
Answer:
feet
Submit Answer
attempt 2 out of 20i

Answer 1

Explanation:

This question is essentially asking to find the adjacent side of a right triangle.

we can set up our right triangle having a hypotenuse of unknown length, an opposite side of 113 (height of lighthouse), and an adjacent side of x.

Using trigonometry we know from SOHCAHTOA that since we know the opposite side and we need the adjacent side, tangent will work perfectly!

Setting it up:

`tan (\theta) = (opposite)/(adjacent)`

∴
`tan(11^(o) ) = (113)/(x)`

We can now rearrange the equation and solve for x.

`x = (113ft)/(tan(11^(o)))`

We now end up with x = 581.3 ft (rounded to the nearest tenth).

Hope this helps!