# Secant: in a Right Triangle

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

## Formula

Secant is the reciprocal of cosine.

So, to find secant (sec A),

first write 1/[cos A],

find cos A = (Adjacent side)/(Hypotenuse),

and write the reciprocal of cos A:

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

## Example

Secant is the reciprocal of cosine.

And cosine is CAH:

Cosine, Adjacent side, Hypotenuse.

But the hypotenuse is unknown.

So set the hypotenuse x

and find x first.

The given triangle is a right triangle.

So, by the Pythagorean theorem,

x^{2} = 1^{2} + 2^{2}.

1^{2} = 1

+2^{2} = +4

1 + 4 = 5

x^{2} = 5

So x = √5.

Square Root

x is the hypotenuse.

So x is plus.

So you don't have to write ±.

Write √5

next to the hypotenuse.

sec A = 1/[cos A]

Find cos A.

Cosine is CAH:

Cosine,

Adjacent side (1),

Hypotenuse (√5).

So 1/[cos A] = 1/[1/√5].

1/[1/√5] = √5

The reciprocal of 1/√5 is

√5/1 = √5.

So sec A = √5.