Questions & Answers

Question

Answers

A.45°

B.30°

C.60°

D.90°

Answer
Verified

Let ABC is a right angle triangle.

∠ ACB =$ \theta$

Let the length of AB = height of tower = x.

So, shadow length = Length of BC = $\sqrt {3x} $.

In ∆ ACB,

$\tan \theta = \dfrac{{Perpendicular}}{{Base}}$

$\tan \theta = \dfrac{{AB}}{{BC}}$

$\tan \theta = \dfrac{x}{{\sqrt {3x} }}$

$\tan \theta = \dfrac{1}{{\sqrt 3 }}$

Tan θ = tan30° $\left( {\tan 30^\circ = \dfrac{1}{{\sqrt 3 }}} \right)$

$ \theta$= 30°

i.e. $Cot \theta= \dfrac{{Base}}{{Perpendicular}}$. The angle of elevation is the angle between the horizontal and a line from your position to the sun.