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