# Tangent Formula

Tangent Angle Formula is normally used to calculate the angle of the right triangle. In a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side.

The tangent function, along with sine and cosine, is one of the three most common trigonometric functions. In any right triangle, the tangent of an angle is the length of the opposite side (O) divided by the length of the adjacent side (A).

In a formula, it is written simply as ‘tan’.

$\large tan\;\theta=\frac{O}{A}$

Where,
O = Opposite side
A = Adjacent side

### Solved Example of Tangent Formula

Example: Calculate the tangent angle of a right triangle whose adjacent side and opposite side are 8 cm and 6 cm respectively?

Solution:

Given,
Adjacent side (A)= 8 cm
Opposite side (O)= 6 cm

Using the formula of tangent: $tan\;\theta=\frac{O}{A}$

$tan\;\theta=\frac{6}{8}$

$tan\;\theta=0.75$

#### Practise This Question

An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth's surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling