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.

Cosine Formula

The Cosine Formula is,

\[\LARGE \cos \theta =\frac{Adjacent}{Hypotenuse}\]

Laws of Cosine

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

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

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

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 ?

Given,  Adjacent side = 12 cm
Hypotenuse = 15 cm

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

$cos \theta$  = $\frac{12 cm}{15 cm}$

$cos \theta$ = 0.8

Practise This Question

What are the necessary characteristics of a weedicide?