A triangle has sides A, B, and C. The angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 12, what is the area of the triangle?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 12, what is the area of the triangle?

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Answer 1 · 2018-03-08T09:00:24

37.5034

Explanation:

First, we find the missing angle $\frac{π}{12}$ $pi/12$ is 15 degrees and $\frac{2 π}{3}$ $(2pi)/3$ is 120 all triangle's angles add up to 180 180-135 and the missing angle is 45 degrees or $\frac{π}{4}$ $pi/4$ now that there is a known side, we can use the sin rule.
$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a/(sin A) = b/sin B = c/sinC$
$c = \frac{b sin C}{sin b}$ $c=(bsinC)/sinb$

$\frac{12 sin 120}{sin 45}$ $(12 sin 120)/ sin 45$ is 8.188160008 side C
for the next side we get 9.170785943 ide A
http://www.teacherschoice.com.au/Maths_Library/Trigonometry/solve_trig_AAS.htm for more details

the area is 37.5034
here is a good online calculator for this
https://www.mathopenref.com/heronsformula.html
and also how I got to this area.

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 12, what is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. The angle between sides A and B is (2pi)/32π3(2pi)/3 and the angle between sides B and C is pi/12π12pi/12. If side B has a length of 12, what is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 12, what is the area of the triangle?