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 48, what is the area of the triangle?

Answer 1

4299.322531

Explanation:

lets draw a perpendicular line on B .
suppose, the length of the perpendicular is D
now, the problem says, the angle between A and B is `(5pi)/12`
now,
in, `triangleABD`,
`D/B=tan((5pi)/12)`
`or,D=Btan((5pi)/12)`
now, by putting the values, B=48 and tan`(5pi)/12` ,
`D=48*3.732050808`
`or, D=179.1384388`
so,
The area of `triangleABC=1/2*B*D`
now, by putting the value of B and D in the above equation, we get,
`triangleABC=1/2*48*179.1384388=4299.322531`