Question

From the top of the light house, an observer looks at a ship and finds the angle of depression to be 30°.If the height of the light-house is 100 meters, then find how far the ship is from the light-house.

Answer 1

Here is your answer in this picture

Answer 2

Answer:

Distance of ship from the lighthouse is = 173.20 m

Step-by-step explanation:

In the question,

Angle of depression of the ship from the top of the lighthouse = 30°

Height of the lighthouse, h = 100 m

Now,

Let, us say the distance of the ship from the base of the lighthouse is = x

So,

From the figure attached below we can say that,

$tan30=\frac{h}{x}\\\frac{1}{\sqrt{3}}=\frac{100}{x}\\So,\\x=100\sqrt{3}\\x=173.20\ m$

Therefore, the distance of the ship from the base of the lighthouse is given by,

x = 173.20 m