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From a boat 300 metres away from a vertical cliff, the angles of elevation of the top and the foot of a vertical concrete pillar at the edge of the cliff are $55 ∘ 40'$ and $54 ∘ 20'$ respectively. Find the height of the pillar correct to the nearest meter.

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90 m

48 m

21 m

72 m

answer is C.

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Detailed Solution

Let’s convert the degrees and minutes in decimal degrees.

54 ∘ 20' = 54 ∘ + 2060 = 54 ∘ + 0.33 ∘ = 54.33 ∘

Similarly,

55 ∘ 40' = 55 ∘ + 4060 = 55 ∘ + 0.67 ∘ = 55.67 ∘

Now, in

Δ A B D

tan 54.33 ∘ = A D A B A D = A B × tan 54.33 ∘ = 300 × 1.39 = 417 m

Then, in

Δ A B C

tan 55.67 ∘ = A C A B A C = A B × tan 55.67 ∘ = 300 × 1.46 = 438 m

The height of the pillar is,

A C − A D = 438 − 417 = 21 m

Hence, the correct option is 3.

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