Cotangent: in a Right Triangle

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

Formula

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

Example

Solution

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,
x2 + 22 = 52.

+22 = +4

52 = 25

Move +4 to the right side.
Then x2 = 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.