Question

From the top of a lighthouse 100 m high the angles of depression of two ships on opposite sides of it are 48° and 36° respectively. Find the distance between the two ships to the nearest metre.

Answer 1

From right angle Δ ADC,

`"AD"/"CD" = tan 36°`

`100/y = tan 36°`

y = `100/tan 36°`

y = `100/(0.7265)`

y = 137.646 m

From right angle Δ ADB,

`100/x = tan 48°`

`x = 100/1.1106`

x = 90.04 m

Distance between the ships = x + y 
= 137.638 + 90.04
= 227.678 m
= 228 m (appro.)