# Cotangent: in a Right Triangle

How to find cotangent in a right triangle (trigonometry): formula, 1 example, and its solution.

## Formula

Cotangent is the reciprocal of tangent.

So, to find cotangent (cot A),

first write 1/[tan A],

find tan A = (Opposite side)/(Adjacent side),

and write the reciprocal of tan A:

1 / [(Opposite side)/(Adjacent side)].

## Example

Cotangent is the reciprocal of tangent.

And tangent is TOA:

Tangent, Opposite side, Adjacent side.

But the side adjacent to ∠A is unknown.

So set the adjacent side x

and find x first.

The given triangle is a right triangle.

So, by the Pythagorean theorem,

x^{2} + 2^{2} = 5^{2}.

+2^{2} = +4

5^{2} = 25

Move +4 to the right side.

Then x^{2} = 21.

Square root both sides.

Then x = √21.

x is the adjacent side.

So x is plus.

So you don't have to write ±.

Write √21

below the adjacent side.

cot A = 1/[tan A]

Find tan A.

Tangent is TOA:

Tangent,

Opposite side (2),

Adjacent side (√21).

So 1/[tan A] = 1/[2/√21].

1/[2/√21] = √21/2

The reciprocal of 2/√21 is

√21/2.

So cot A = √21/2.