Question

A triangle has sides A, B, and C. Sides A and B are of lengths `1` and `2`, respectively, and the angle between A and B is `pi/4`. What is the length of side C?

Answer 1

≈ 1.5

Explanation:

In this triangle , know 2 sides and the angle between them , so use 'cosine rule'

for this triangle the cosine rule is :

`C^2 = A^2 + B^2 -(2ABcos(pi/4))`

`= 1^2 + 2^2 - ( 2 xx 1 xx 2 xx 1/sqrt2 )`

= 1 + 4 - `(4sqrt2)/2 = 5 - 2 sqrt2 ≈ 2.17`

now`C^2 ≈ 2.17 rArr C = sqrt2.17 ≈ 1.5`