Question

From the top of a lighthouse, 40m above the water, the angle of depression of a small boat is 20o. Estimate how far the boat is from the base of the lighthouse ?

Answer 1

Given,

The height of the lighthouse is 40 metres

angle of depression of a small boat is 20°

To find,

The distance between the boat and the base of the lighthouse.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Here, we have to apply the Trigonometry.

If we compare the whole scenario with a right angled triangle, then we will get that,

Height = height of the lighthouse= 40 m

Base = Distance between lighthouse and boat = x metre (let)

Angle of elevation of the lighthouse from the boat = Angle of depression of the boat from lighthouse = 20°

Now,

height/base = tan ∅

40/x = tan 20° (putting the values)

40/x = 0.364

x × 0.364 = 40

x = 109.89

Hence, the approximate distance between the lighthouse and boat is 109.89 metres.