Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/6` and the angle between sides B and C is `pi/12`. If side B has a length of 21, what is the area of the triangle?

Answer 1

`angleB =pi-((5pi)/6 +pi/12) = pi/12, a/sin(pi/12) = 21/sin(pi/12) -> a = 21/sin(pi/12) * sin(pi/12) = 21`
`Area = 1/2 ab sin C = 1/2 (21)(21)sin( (5pi)/6) = 110.25 unit^2`

Explanation:

First, add the two given angles and subtract from `pi` to get the third angle. Then find one of the other two sides. In this case I found side a by using the sine rule. So to find the area of the triangle I use side a and b and angle C and substitute in to the angle formula then calculate.