Question

16) The angle of elevation from a ship to the top of a lighthouse is 5°. If the ship is 1500 m from the lighthouse, how tall is the lighthouse?A. Draw and label a diagram. (1 point)B. Set up trig equation. (1 point)C. Determine the height of the lighthouse. Round to the nearest meter. (1 point)

Answer 1

A.

Drawing a diagram to represent this problem, we have:

B.

The trigonometric equation we should use to find the height of the lighthouse can be found using the tangent relation of the angle 5°.

The tangent is equal to the length of the opposite leg to the angle over the length of the adjacent leg to the angle.

So we have:

$\tan5°=\frac{h}{1500}$

C.

Solving the trigonometric equation for h, we have:

$\begin{gathered} 0.0875=\frac{h}{1500}\\ \\ h=1500\cdot0.0875\\ \\ h=131.25\text{ m} \end{gathered}$

Rounding to the nearest meter, we have a height of 131 meters.