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Question

The angle of elevation of the top of a mountain observed from each of the three points A,BandC forming a triangle ABC on the plane is α. The height of the mountain is


A

ɑ1tanɑcotA

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B

ɑ2cotɑtanA

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C

ɑ2tanɑcosecA

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D

ɑ2cosecɑtanA

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Solution

The correct option is C

ɑ2tanɑcosecA


Explanation for the correct option.

Finding the height of the mountain

Given: The angle of elevation of the top of a mountain observed from each of the three points A,BandC forming a triangle ABC on the plane is α

Here, the Height of the tower=PQ

Circumradius =QA=QB=QC=R

We know tanθ=oppositeadjacent,So

In triangle QAP, we get

tan(QAP)=QPQAtanα=QPRQP=Rtanα

Height of tower =Rtanα.

R=ɑ2sinAh=ɑ2tanɑcosecA

Hence the correct answer is option (C)


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