Angle of Elevation

The angle of elevation is a widely used concept related to height and distance. An angle of elevation is defined as an angle between the horizontal plane and oblique line from the observer’s eye to some object above his eye. Eventually, this angle is formed above the surface. As the name itself suggests, the angle of elevation is so formed that it is above the observer’s eye. Solving the angle of elevation is used in finding distances, heights of buildings, towers etc with the help of trigonometric ratios.

Angle of Elevation Definition

Angle of Elevation

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

Angle of Elevation Formula

The formula for finding the angle of elevation depends on knowing the information such as the measures of the opposite, hypotenuse, and adjacent side to the right angle. If the distance from the object and height of the object is given, then the formula for the angle of elevation is given by

Tangent of the angle of elevation = Height of the Object / Distance from the object

Angle of Elevation Related Terms

The three terms related to the angle of elevation are

  • Angle
  • Horizontal Line
  • Line of sight

Angle

If two rays or two line segments meet at a common endpoint, then the point is known as the vertex. Two straight lines meet at a common point is said to form an angle. Angle play an important role, and some other definitions of angle are:

  • The angle is a gap in between two lines which connect on one side.
  • The angles are measured in degrees.

Horizontal Line

A straight line on the coordinate flat surface where all points on the line have the same y-coordinate. The angle and horizontal line combine to form the angle of elevation.

Line of Sight

The line which is drawn from the eyes of the observer to the point being viewed on the object is known as the line of sight.

Angle of Elevation Example

Question:

Find the value of θ in the given figure.

Angle of Elevation Example

Solution:

Given:

In the given triangle ABC, AC = 335 ft, BC = 249 ft

To find ∠A = θ

tan θ = Opposite side/ Adjacent side

tan θ = BC / AC

tan θ = 249/ 335

tan θ = 0.74

Therefore, θ = tan-1 (0.74) = 36

Hence, the value of θ = 36 degrees.

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