Question

A boat is heading towards a lighthouse, where Dalvin is watching from a vertical distance of 138 feet above the water. Round your answer to the nearest tenth of a foot if necessary.

Answer 1

Based on the information, the distance from point A to point B us 459.7 feet

How to find the distance

To find the distance from point A to point B, we can use trigonometry.

From point A

Angle of depression = 13°

Vertical distance = 138 feet

Using the tangent function, we have:

distance A = 138 / tan 13

From point B

Angle of depression = 45°

Vertical distance = 138 feet

distance B = 138 / tan 45

From point A to point B

= distance A - distance B

= (138 / tan 13 ) - (138 / tan 45)

= 459.7 ft

Answer 2

To find the first distance we use:

`\begin{gathered} tan13=(138ft)/(x) \\ x=(138ft)/(tan13º) \\ x=(138ft)/(0.23) \\ x=\text{ 600ft} \end{gathered}`

For the second distance, we change 13º to 45º and 77º to 45º as well.

So:

`\begin{gathered} tan45=(138ft)/(x) \\ 1=(138ft)/(x) \\ x=138ft \end{gathered}`

So the distance from point A to B is=600ft - 138ft = 462ft