A clock tower stands at the crossing of two roads which point in the n

| A clock tower stands at the crossing of two roads which point in the north-south and the east-west directions. P, Q, R and S are points on the roads due north, east, south and west respectively, where the angles of elevation of the top of the tower are respectively, α, β, γ and δ. Then  is equal to:

A.

B.

C.

D.

Right Answer is: B

SOLUTION

Let OA be straight tower.

P, Q, R and S are points on the roads due north, east, south and west

respectively.

In Δ POQ and Δ ORS

So

AOQ = 90° ……….. as OA is straight tower.

AOP = 90° = AOR = AOS

Now Angle of elevation are α, β, γ and δ.

In right angle Δ AOP:

And APO = α

Tanα = AO/OP

OP = AO cotα

Similarly, in Δ AOS:

AOS = 90° and ASO = δ

Tanδ = AO/OS

OS = OA cotδ

And OQ = AO cotβ

And OR = AO cot γ

So, the value

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