Height and Distance Shortcut and Tricks

 Type 1: Find the distance/height/base/length when angle is given

Question 1. A boy is flying a kite in the evening. The thread of the kite was 120 m long and the angle of elevation with the boy’s eyes was 30°. Find the height of the kite?

Options.

A. 30 m

B. 60 m

C. 40 m

D. 55 m

Solution:

Sin 30° = Perpendicular/Hypotenuse = \frac{AB}{AC}

\frac{1}{2} = \frac{h}{120}

h = 60 m

Correct option: B

Type 2: Find the angle when distance/height/base/length is given

Question 2. Find the angle of elevation of the sun when the shadow of a pole of 18 m height is 6\sqrt{3} m long?

Options.

                    A. 45°

                   B. 60°

                   C. 30°

                   D. 90°

Solution:

Let AB be the pole and CB be the shadow

Given that AB = 18 m and CB = 6\sqrt{3}

Let the angle of elevation, ACB = θ

From the right ΔABC,

Tan θ = Perpendicular/Base = \frac{AB}{AC} = \frac{18}{6\sqrt{3}} =\frac{3}{\sqrt{3}}= \sqrt{3}

Therefore,

θ =tan^–¹(\sqrt{3})=60°

Correct option: B