| 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