Question

A triangle has sides A, B, and C. Sides A and B are of lengths `14` and `12`, respectively, and the angle between A and B is `(5pi)/8`. What is the length of side C?

Answer 1

≈ 21.647 units

Explanation:

Given a triangle with 2 sides and the angle between them known, find the 3rd side using the `color(blue)" cosine rule "`

`c^2 = a^2 + b^2 - (2ab costheta)`

where c is the side to be found , a and b are the known sides and `theta " is the angle between them "`

here a = 14 , b = 12 and `theta = (5pi)/8`

hence `c^2 = 14^2 + 12^2 -( 2xx14xx12 cos((5pi)/8))`

`= 196+144 + 128.582...` ≈ 468.582

`rArr c = sqrt468.582 ≈ 21.647 " units "`