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 15, what is the area of the triangle?

Answer 1

`=30`

Explanation:

This is a right angled triangle where `B=15`
Therefore
Angle between `A` and `C` is `pi-(pi/2+pi/12)=5pi/12`
`A/sin(pi/12)=B/sin(5pi/12)`
or
`A/sin(pi/12)=15/sin(5pi/12)`
or
`A=15/sin(5pi/12)(sin pi/12)`
or
`A=15(0.268)`
or
`A=4`
Therefore
Area of the triangle`=1/2(15)(4)`
`=60/2`
`=30`