Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/4` and the angle between sides B and C is `pi/12`. If side B has a length of 24, what is the area of the triangle?

Answer 1

`=60.86squnit`

Explanation:

Let the length of the perpendicular dropped on side B from opposite corner be h.And this perpendicular divides sides B(=24) in two parts.Let the length of one part towards angle `pi/4` be
x and the length of the other part towards angle `pi/12` be y.

So `x/h=cot(pi/4)=>x=h`

And `y/h=cot(pi/12)=>y=hcot(pi/12)`

But by the given condition
`x+y=24`
`=>h+hcot(pi/12)=24`
`:.h=24/(1+cot(pi/12))`

So area of the triangle

`"Area"=1/2*B*h=1/2xx24xx24/(1+cot(pi/12))`

`=60.86squnit`