Question

from the top of the Lighthouse 100 M high the angle of depression of two ships on opposite sides of it are 48 degree and 36 degree respectively find the distance between the two ships correct to the nearest metre

Answer 1

228m is the required answer

hope it helps

Answer 2

The distance between the two ships 228m

Height of the Lighthouse 100M (Given)

Angle of depression = 1 = 48° (Given)

Angle of depression = 2 = 36° (Given)

In ΔADC

AD/CD = tan 36˚

100/y = tan 36˚

y = 100/tan 36˚

= 100/0.7265

y = 137.646 m

Similarly,

From ΔADB,

100/x = tan 48˚

x = 100/1.1106

= 90.04 m

Distance between both the ships = x + y

= 137.638 + 90.04

= 227.678

Thus, the distance between the two ships correct to the nearest metres will be  228 m