If the length of the shadow on the ground of a pole is $\sqrt{3}$ times the height of the pole, then

Question

If the length of the shadow on the ground of a pole is $\sqrt{3}$ times the height of the pole, then the angle of elevation of the Sun is :\

Professor PC Thomas Classes · Answer

(a): Let $A B$ be the height of pole and $B C$ be the length of its shadow. $$ B C=\sqrt{3} A B $$ Let angle of elevation of sun be $	heta$.\ In $	riangle A B C$, we have, $	an 	heta=\frac{A B}{B C}$\ $\Rightarrow \quad 	an 	heta=\frac{A B}{\sqrt{3} A B}$\ $\Rightarrow 	an 	heta=\frac{1}{\sqrt{3}}=	an 30^{\circ} \Rightarrow 	heta=30^{\circ}$\