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Question

From the top of a hill h meters high, the angles of depressions of the top and the bottom of a pillar are α and β, respectively. The height (in metres) of the pillar is


A

h[tanβtanα][tanβ]

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B

h[tanαtanβ][tanα]

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C

h[tanα+tanβ][tanβ]

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D

h[tanα+tanβ][tanα]

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Solution

The correct option is A

h[tanβtanα][tanβ]


Explanation for the correct option:

Step 1. Draw the figure according to the question:

From the figure, we have

tanβ=hx — (1)

tanα=h1x — (2)

Step 2. Equate equation (1) and (2):

htanβ=h1tanα

h1=htanαtanβ

As we can see in the figure,

The height of the pillar =hh1

=hhtanαtanβ

=h1tanαtanβ

=h[tanβtanα][tanβ]

Hence, Option ‘A’ is Correct.


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