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

Question

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

Infinity Learn · Accepted Answer

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 $$tan$$θ$$=hx$$  and $$tan$$θ$$=h+6x+23$$∴  $$hx=h+6x+23$$ $$hx+23h=hx+6x$$         ⇒$$23h=6x$$         ⇒$$x=h3$$∴  $$tan$$θ$$=hx$$         ⇒$$tan$$θ$$=3$$         ⇒θ$$=600$$

If a flag-staff of 6 meters height placed on the top of a tower throws a shadow of 2 $\sqrt{3}$ meters along the ground then the angle (in degrees) that the sun makes with the ground is

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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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If a flag-staff of 6 meters height placed on the top of a tower throws a shadow of 2 $\sqrt{3}$ meters along the ground then the angle (in degrees) that the sun makes with the ground is