Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/2` and the angle between sides B and C is `pi/12`. If side B has a length of 17, what is the area of the triangle?

Answer 1

`angle B =pi-(pi/2 + pi/12)=(5pi)/12,-> a/sinA = b/sinB->a/sin(pi/12) = 17/sin((5pi)/12)->a=(17 sin(pi/12))/sin((5pi)/12) =4.555...`
`Area triangle = 1/2(a)(b)sinC=1/2(4.555...)(17)sin(pi/2)~~38.72`

Explanation:

First subtract the given angles from `pi` to find the third angle. In order to find the area of the triangle we need to find the measurement of one of the other two sides. So I use the law of sines to find side a and then put it into the area formula and calculate. Note I use angle C since sides a and b are in my calculation.