Question

A boat is heading towards a lighthouse, where Jack is watching from avertical distance of 108 feet above the water. Jack measures an angle ofdepression to the boat at point A to be 9. (9 degrees). At some later time,Jack takes another measurement and finds the angle of depression to theboat (now at point B) to be 66. (66 degrees). Find the distance frompoint A to point B. Round your answer to the nearest tenth of a foot ifnecessary.

Answer 1

Given

A boat is heading towards a lighthouse, where Jack is watching from a

vertical distance of 108 feet above the water.

Jack measures an angle of depression to the boat at point A to be 9°.

At some later time, Jack takes another measurement and finds the angle of depression to the boat (now at point B) to be 66°.

To find: The distance from point A to point B.

Explanation:

It is given that,

A boat is heading towards a lighthouse, where Jack is watching from a

vertical distance of 108 feet above the water.

Jack measures an angle of depression to the boat at point A to be 9°.

At some later time, Jack takes another measurement and finds the angle of depression to the boat (now at point B) to be 66°.

That imples,

Then,

$\begin{gathered} \tan9=\frac{108}{AC} \\ AC=\frac{108}{\tan9} \\ AC=681.89ft \end{gathered}$

Also,

$\begin{gathered} \tan66=\frac{108}{BC} \\ BC=\frac{108}{\tan66} \\ BC=48.08ft \end{gathered}$

Therefore,

$\begin{gathered} AB=AC-BC \\ =681.89-48.08 \\ =633.81ft \\ =633.8ft \end{gathered}$

Hence, the distance from point A to point B is 633.8ft.