# Cosine Formula

In trigonometry, the law of cosines is also known as the cosine formula or cosine rule, relates the lengths of the sides of a triangle to the cosine of one of its angles.

The Cosine Formula is,

$\LARGE \cos \theta =\frac{Adjacent}{Hypotenuse}$

$\large a^{2}=b^{2}+c^{2}-2bc.\cos A$

$\large b^{2}=a^{2}+c^{2}-2ac.\cos B$

$\large c^{2}=a^{2}+b^{2}-2ab.\cos C$

### Solved Examples

Question 1: Calculate the cosine angle of a right triangle given the adjacent side and hypotenuse are 12 cm and 15 cm respectively ?
Solution:

Given,  Adjacent side = 12 cm
Hypotenuse = 15 cm

$cos \theta$ = $\frac{Adjacent}{Hypotenuse}$

$cos \theta$  = $\frac{12 cm}{15 cm}$

$cos \theta$ = 0.8

 Related Links Area Of A Square Formula Percent Error Formula Limit Formula Arc Length Formula Beat Frequency Formula Complex Number Formula Ideal Gas Law Formula Angular Speed Formula Rotational Kinetic Energy Formula Mechanical Energy Formula