Question

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

Answer 1

≈ 11.745 units

Explanation:

In this situation where we have a triangle with 2 sides and the angle between them known , and we wish to find the 3rd side , then we use the `color(blue)" cosine rule "`

`c^2 = a^2 + b^2 - (2abcosC)`

where a and b are the 2 given sides and C , the angle between them. c , is the side to be found.

here a = 12 , b = 5 and C `= (5pi)/12`

substitute these values into the `color(blue)" cosine rule "`

`c^2 = 12^2 + 5^2 - (2xx12xx5xxcos((5pi)/12))`

`= 144 + 25 -( 120cos((5pi)/12))= 169 -(31.058)`

now `c^2 = 137.942 rArr c = sqrt137.942 ≈ 11.745 " units "`