From the top of the lighthouse, 40m above the water, the angle of depression of a small boat is 60⁰. Find how far the boat is from the base of the lighthouse. 

 

 

Given that, 

Height of the light house is 40 m

Angle of depression is 60⁰

Let the distance between the boat and lighthouse is x

In ΔABC we get, 

$\tan 60⁰=\frac{ AB}{BC}$

$\Rightarrow \sqrt{3} = \frac{40}{x}$

$\Rightarrow 𝑥 = \frac{40 }{\sqrt{3}} 𝑚$

$\Rightarrow 𝑥 = \frac{40 \sqrt{3}}{ 3} m$

Hence the boat is $\Rightarrow 𝑥 = \frac{40 \sqrt{3}}{ 3} m$ from the base of the lighthouse