Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(7pi)/12`, the angle between sides B and C is `pi/6`, and the length of B is 5, what is the area of the triangle?

Answer 1

Area=`8.53766` square units

Explanation:

From the given, two angles `A=pi/6`, `C=(7pi)/12` and included side `b=5`. Try drawing the triangle. See that angle `B=pi/4` by computation using the formula `A+B+C=pi`. Also , the altitude from angle C to side c can be called height `h` is `h = b*sin (pi/6)=2.5`
Side `c` can be computed using formula `c=b*cos A+h*cot B`.
`c=5*cos (pi/6)+2.5*cot (pi/4)`=`2.5*(sqrt3+1)`

`c=2.5(sqrt3+1)`
Area can now be computed

Area`=1/2*b*c*sin A`

Area`=1/2*5*(2.5(sqrt3+1))*sin (pi/6)`

Area`=8.53766` square units