The length of the shadow of a pole inclined a | vedclass

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(A) Let $OP = l$ be the length of the pole,inclined at $10^\circ$ to the vertical. Let $O$ be the base of the pole and $S$ be the tip of the shadow. T

Vedclass · Accepted Answer

$\frac{2.05 \sin 38^\circ}{\sin 42^\circ}$

Vedclass · Answer

(A) Let $OP = l$ be the length of the pole,inclined at $10^\circ$ to the vertical. Let $O$ be the base of the pole and $S$ be the tip of the shadow. The shadow length $OS = 2.05 	ext{ m}$.In $	riangle SPO$,the angle of elevation of the sun is $\angle OSP = 38^\circ$.The angle between the pole and the vertical is $10^\circ$. The angle between the vertical and the ground is $90^\circ$.Thus,the angle between the pole and the ground is $\angle SOP = 90^\circ + 10^\circ = 100^\circ$.The sum of angles in $	riangle SPO$ is $180^\circ$,so $\angle SPO = 180^\circ - (38^\circ + 100^\circ) = 180^\circ - 138^\circ = 42^\circ$.Using the Sine Rule in $	riangle SPO$:$\frac{OP}{\sin \angle OSP} = \frac{OS}{\sin \angle SPO}$$\frac{l}{\sin 38^\circ} = \frac{2.05}{\sin 42^\circ}$$l = \frac{2.05 \sin 38^\circ}{\sin 42^\circ}$

The length of the shadow of a pole inclined at $10^\circ$ to the vertical towards the sun is $2.05 \text{ m}$,when the elevation of the sun is $38^\circ$. The length of the pole is

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