Height and Distance Tips and Tricks for Government Exams

Height Definition

The measurement of an object in the vertical direction known as Height.

Distance Definition

The measurement of an object from a particular point in the horizontal direction Known as Distance .

How to solve word problems that involve angle of elevation or depression Shortcuts and Easy Tips & Tricks to solve questions

• Step 1: Draw a sketch of the situation given.
• Step 2: Mark in the given angle of elevation or depression and other information.
• Step 3: Use trigonometry to find the required missing length.

Height and Distance Tips and Tricks & Shortcuts

There are two primary ways to express the angular relationship between the height of an object and an observer's line of sight:

• Angle of Elevation: This refers to the angle formed between the horizontal line and the line of sight from the observer's eye to an object situated above the observer.
• Angle of Depression: When the object is positioned below the observer's level, the angle between the horizontal line and the observer's line of sight to the object is termed the angle of depression.

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

Example: 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?
(a) 30 m
(b) 60 m
(c) 40 m
(d) 55 m
Ans: (b)
Sin 30° = Perpendicular/Hypotenuse = AC/AB  
1/2 = ℎ/120
h = 60 m

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

Example: Find the angle of elevation of the sun when the shadow of a pole of 18 m height is 6√3 m long?
(a) 45°
(b) 60°
(c) 30°
(d) 90°
Ans: (b)
Let AB be the pole and CB be the shadow
Given that AB = 18 m and CB = 6√3
Let the angle of elevation, ACB = θ
From the right ΔABC, Tan θ = Perpendicular/Base =
Therefore, θ = tan^–1(√3) = 60°