Question

A man standing on the deck of a ship, which is 10 m above the water level observes the angle of elevation of the top of a hill as 60° and angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.

Answer 1

Step-by-step explanation:

Let AB=10m, cliff of a ship where man is standing

Let CE be the hill.

CD=AB=10m

In △ADE

$$\tan 60°=\cfrac { h }{ x } $$

3x=h

x=3h⟶(1)

In △ABC

$$\tan 30°=\cfrac { 10 }{ x } $$

31=x10

x=103⟶(2)

We have two equations (1) & (2), Multiplying them we get,

x2=10h

h=30m

∴CE=CD+DE=10+30=40m

Answer 2

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