Q.

If a flag-staff of 6 meters height placed on the top of a tower throws a shadow of  23 meters along the ground then the angle (in degrees) that the sun makes with the ground is

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a

600

b

300

c

450

d

750

answer is A.

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Detailed Solution

Let OA and AB be the shadows of tower OP and flag staff PQ respectively on the ground. Suppose the sun makes an angle  θ with the ground.Let OA=x . In triangles OAP and OBQ, we have tanθ=hx  and tanθ=h+6x+23∴  hx=h+6x+23 hx+23h=hx+6x         ⇒23h=6x         ⇒x=h3∴  tanθ=hx         ⇒tanθ=3         ⇒θ=600
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