Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/12` 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

`=28.13`

Explanation:

The angle between `A` and `C` `=pi-((5pi)/12+pi/12)=pi-pi/2=pi/2`
This shows that triangle is right-angled with hypotenuse `=B=15`
Hence `height=`side `A=15sin(pi/12)` and `base=`side `B=15cos(pi/12)`
Therefore Area of the triangle`=1/2times height times base`
`=1/2times15sin(pi/12)15cos(pi/12)`
`=225/2(0.2588)(0.966)`
`=28.13`