Angle‌ ‌of‌ ‌elevation‌

The angle of elevation is a concept of trigonometry. It is widely used to analyze the distance of an object or a point with respect to anything stationary. The angle of elevation can be defined as the angle formed between the plane of horizon and the point being observed in context to the observer who is fixed. For example, an airplane is flying past a person who is standing on the ground. If the person looks at the airplane in the sky, the angle of inclination thus formed is called as the angle of elevation with respect to the observer at rest.

The angle of inclination has great use in trigonometry and applications of trigonometry in questions involving the distance or height of a buildings, towers etc. with respect to an observer or any fixed point.

For example,

The above figure represents the angle of elevation formed with respect to a fixed point A. Here, θ is the angle of elevation, line s is the line of sight and h is the horizontal line.

Important terms

There are some points which must be considered.

Angle of elevation: Angle of elevation is the angle between the horizontal line and the line of sight. It is formed at the vertex of intersection of the horizontal line and line of sight. It is the same angle as used in trigonometry. It can be obtained by using the trigonometric ratios sine, cosine, tan, cot, sec and cosec. Also, for a given angle of elevation, values of trigonometric ratios can also be calculated.
Line of sight: The line of sight is the line which is formed between the eye of an observer and the object at which the observer is looking.
Horizontal line: The horizontal or horizontal line is an imaginary line which forms the base of the angle of elevation. It is considered at the same level as the observer.

Formula for angle of elevation

The formula of angle of elevation depends upon the values given. For example, for a building of a given height and distance from the observer

Angle of elevation = height of building, and the distance of building from the observer

We know,

tan θ = height/distance

Substituting the value of tan θ, we get

Angle of elevation = tan θ

Hence,

tan θ = height of building/distance of building from the observer

in general,

tan θ = height of the given entity/distance of the given entity

However, the value of the angle of elevation can change depending on the given values. For example, for a given distance and measure of the line of sight, then the angle of elevation becomes

Angle of elevation = cos θ

Since,

Cos θ = hypotenuse(line of sight)/base(distance from observer)