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?

1 Answer
P dilip_k
Jul 20, 2016

=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

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