Question

The length of shadow of a tower on the plane ground is times the height of the tower. The angle of elevation of sun is :

• A. 45⁰
• B. 30⁰
• C. 60⁰
• D. 90­⁰

Answer 1

The correct option is B

30⁰

Let AB be the tower and BC be the length of the shadow of the tower.
Here, $\theta$, is the angle of elevation of the sun.
Given, length of shadow of tower =$\sqrt{3}\times$ Height of the tower.
$BC=\sqrt{3}AB....\left(1\right)$
In right $\Delta ABC$,
$tan\theta =\frac{AB}{BC}[tan\theta =\frac{Oppositeside}{Adjacentside}]tan\theta =\frac{AB}{\sqrt{3AB}}\left[Using\right(1\left)\right]\Rightarrow tan\theta =\frac{1}{\sqrt{3}}\Rightarrow tan\theta =tan{30}^{\circ }[\therefore tan{30}^{\circ }=\frac{1}{\sqrt{3}}]\Rightarrow \theta ={30}^{\circ }$
Thus, the angle of elevation of the sun is ${30}^{\circ }$.