Question

From the top of a 150 m high cliff, the angles of depression of two boats on thewater are 20° and 25°. How far apart are the boats? Show your work.

Answer 1

Given

From the top of a 150 m high cliff, the angles of depression of two boats on the

water are 20° and 25°.

To find:

How far apart are the boats?

Step-by-step explanation:

It is given that,

From the top of a 150 m high cliff, the angles of depression of two boats on the water are 20° and 25°.

That implies,

Then,

`\begin{gathered} \tan20\degree=(150)/(x+y) \\ x+y=(150)/(0.36397) \\ x+y=412.1216 \\ \tan25\degree=(150)/(x) \\ x=(150)/(0.46631) \\ x=321.676 \end{gathered}`

Therefore,

`\begin{gathered} y=x+y-x \\ y=412.122-321.676 \\ y=90.45m \end{gathered}`

Hence, the two boats are 90.45m apart.