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?
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,
[tex]\begin{gathered} \tan20\degree=\frac{150}{x+y} \\ x+y=\frac{150}{0.36397} \\ x+y=412.1216 \\ \tan25\degree=\frac{150}{x} \\ x=\frac{150}{0.46631} \\ x=321.676 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y=x+y-x \\ y=412.122-321.676 \\ y=90.45m \end{gathered}[/tex]Hence, the two boats are 90.45m apart.
