A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{6}$ $(5pi)/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . 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 $= 182.25$ $=182.25" " "$ square units

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

We need the height $h$ $h$ to solve for the Area $= \frac{1}{2} b h$ $=1/2bh$

Solve h

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

$h = \frac{b}{cot A + cot C}$ $h=b/(cot A+cot C)$

$h = \frac{27}{cot (\frac{π}{12}) + cot (\frac{5 π}{6})}$ $h=27/(cot (pi/12)+cot ((5pi)/6)$

$h = 13.5$ $h=13.5$

Solve Area:

Area $= \frac{1}{2} b h$ $=1/2 b h$

Area $= \frac{1}{2} (27) (13.5$ $=1/2(27)(13.5$

Area $= 182.25$ $=182.25" "$ square units

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A triangle has sides A, B, and C. The angle between sides A and B is 5π6(5pi)/6 and the angle between sides B and C is π12pi/12. If side B has a length of 27, what is the area of the triangle?