A triangle has sides A, B, and C. The angle between sides A and B is $(5pi)/6$ and the angle between sides B and C is $pi/12$ . If side B has a length of 27, what is the area of the triangle?

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Answer 1 · 2016-02-21T05:53:26

Area $=182.25" " "$ square units

We will take the side $b=27$ as the base of the triangle
Angle $A=pi/12$ and angle $C=(5pi)/6$

We need the height $h$ to solve for the Area $=1/2bh$

Solve h

$b=h*cot A + h cot C$

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

$h=27/(cot (pi/12)+cot ((5pi)/6)$

$h=13.5$

Solve Area:

Area $=1/2 b h$

Area $=1/2(27)(13.5$

Area $=182.25" "$ square units

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A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/6(5pi)/6 and the angle between sides B and C is pi/12pi/12. If side B has a length of 27, what is the area of the triangle?