Question 5

# The height of a light house is 20 meters above sea level. The angle of depression (from the top of the lighthouse) of a ship in the sea is 30°. What is the distance of the ship from the foot of the light house?

Solution

angle of depression = 30° = angle of elevation from the boat

height of light house = 20m

let the distance btw the light house and boat be x

tanФ= $$\frac{opp}{adj}$$

tan30°= $$20\div \text{distance btw the light house and boat}$$

$$\dfrac{1}{\sqrt{3}}=20\div x$$

x=$$20\sqrt{3}$$