A triangle has sides A, B, and C. The angle between sides A and B is $pi/3$ and the angle between sides B and C is $pi/12$ . If side B has a length of 42, what is the area of the triangle?

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Answer 1 · 2016-01-26T09:17:34

Area $=204.669$ square units

Solve for the altitiude $h$ from angle $B$ to side $b$ :

$b=h cot A + h cot C$
$b=h(cot A+cot C)$

$h=b/(cot A+cot C)=42/(cot pi/12+cot pi/3)$

$h=9.74613$

Solve the Area:

Area $=1/2*b*h$

Area $=1/2*(42)(9.74613)$

Area $=204.669$ square units

A triangle has sides A, B, and C. The angle between sides A and B is pi/3pi/3 and the angle between sides B and C is pi/12pi/12. If side B has a length of 42, what is the area of the triangle?