Question

From the top of a lighthouse the angles of depression of two ships on opposite sides of the lighthouse were observed to be 60°and 45°. If the height of the lighthouse is 100 m and the foot of the lighthouse is in line with the ships, find the distance between the two ships. ​

Answer 1

From right angled △ABC,

tan 30˚ = AC/BC

⇒ 1/√3 = 90m/BC

⇒ BC = [90 × √3] m

∴ BC = 155.88 m

Again from right angled △ACD,

tan 45˚ = AC/CD

⇒ 1 = 90 m/CD

⇒ CD = 90 m

Hence, the distance between the two ships = BC + CD = (155.88 + 90) m

= 245.88 m