Question

A triangle has sides A, B, and C. Sides A and B are of lengths `1` and `8`, respectively, and the angle between A and B is `(5pi)/8`. What is the length of side C?

Answer 1

C ≈ 8.43

Explanation:

In this triangle , 2 sides and the angle between them are known , hence use the`color(blue)(" cosine rule ")`

`C^2 = A^2 + B^2 - (2ABcostheta)`

here A = 1 , B = 8 and `theta = (5pi)/8`
substitute these values into the formula

`C^2 = 1^2 + 8^2 - ( 2 xx 1 xx 8cos((5pi)/8) )`

= 1 + 64 - ( -6.12) = 65 + 6.12 = 71.12

`C^2 = 71.12 rArr C =sqrt(71.12) ≈ 8.43`