Cosine: in a Right Triangle
How to find cosine in a right triangle (trigonometry): formula, 3 examples, and their solutions.
Formula
Cosine is the ratio of
[Adjacent side]/[Hypotenuse]
in a right triangle.
The adjacent side means
the side adjancent to ∠A
(which is not the hypotenuse).
To remember the ratio,
remember CAH:
Cosine, Adjacent side, and Hypotenuse.
Example
Cosine is CAH:
Cosine, Adjacent side, and Hypotenuse.
The Adjacent side is 4.
The Hypotenuse is 5.
So,
C, cos A
is equal to,
A: adjacent side, 4
over,
H: hypotenuse, 5.
So cos A = 4/5.
Example
Cosine is CAH:
Cosine, Adjacent side, and Hypotenuse.
The Adjacent side is 5.
The Hypotenuse is 13.
So,
C, cos A
is equal to,
A: adjacent side, 5
over,
H: hypotenuse, 13.
So cos A = 5/13.
Example
First, find cos A
from the given right triangle.
Cosine is CAH:
Cosine, Adjacent side, and Hypotenuse.
The Adjacent side is 6.
The Hypotenuse is x.
So,
C, cos A
is equal to,
A: adjacent side, 6
over,
H: hypotenuse, x.
Next, it says
cos A = 3/5.
So write
[ = 3/5].
So cos A = 6/x = 3/5.
Solve 6/x = 3/5.
Then 3x = 30.
Divide both sides by 10.
Then x = 10.
So x = 10.