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^@`

`=> 100/tan 36^@  = 100/0.7265`  

`=> y = 137.638 m`

From right angle Δ ADB

`100/x = tan 48^@ => x = 100/1.1106 = 90.04 m`

∴ Distance between the ships = x + y

= 137.638 + 90.04 = 227.678 m

= 228 m (approx)