Question

A man on deck of a ship 12m above water observes the angle of elevation of the top of a cliff to be 60° and angle of depression of the base to be 30°. Find the height of the cliff

Answer 1

tan 30°=12÷x

1/√3=12÷x

X=12√3m

tan 60°=y÷x

√3=y÷12√3

y=36m

Total height of cliff= 36+12

=48m

Answer 2

Let AB be the ship and CD be the cliff.

Now from the figure, DE=AB=12m

In ∆ DEA,

DE/AE = tan 30°

12/AE = 1/√3

AE = 12√3 m

In ∆ CEA,

CE/AE = tan 60°

CE/ 12√3 = √3

CE = 36 m

Now, CD = CE + DE

= 36 + 12 = 48 m

Length of the cliff = 48 m