Question

A man on the deck of a ship is 10 m above water level. He observes that the angle of elevation of the top of a cliff is 42° and the angle of depression of the base is 20°. Calculate the distance of the cliff from the ship and the height of the cliff.

Answer 1

Let the height of the cliff be h meters and the distance of the cliff from the ship be x meters.

In right-angled ΔQRS,
∴ QR = ST = 10 m
TQ = RS = x m

∴ tan 70° = `"RS"/"QR"`

⇒ `2.747 = x/(10 m)`

∴ x = 27.47 m
Hence, the distance of the cliff from the ship = 27.47 m

Again in right angled ΔPRS,
∴ tan 42° = `"PR"/"RS"`

⇒ `0.9004 = "PR"/27.47`

⇒ PR = [0.9004 × 27.47] m

⇒ PR = 24.73 m

∴ PQ = PR + RQ

PQ = [24.73 + 10] m

PQ = 34.73 m

Hence the height of the cliff = 34.73 m.