A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 13, what is the area of the triangle?

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 13, what is the area of the triangle?

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Answer 1 · 2016-02-16T03:42:58

(169 $\sqrt{}$ $sqrt$ 6 / 8) cosec ( $\frac{π}{12}$ $pi/12$ ) = 200, areal units, nearly

Explanation:

Using lower case letters a, b and c for angles and a + b + c = $π$ $pi$ ,
.with a = $\frac{π}{4}$ $pi/4$ and c = $2 \frac{π}{3}$ $2pi/3$ , b = $\frac{π}{12}$ $pi/12$ .
Using B/sin(b) = A/sin(a), A = 13 sin( $\frac{π}{4}$ $pi/4$ ) / sin ( $\frac{π}{12}$ $pi/12$ )
Using, area = base X altitude / 2, the answer is B X A X sin (c) / 2.

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 13, what is the area of the triangle?

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A triangle has sides A,B, and C. If the angle between sides A and B is 2π3(2pi)/3, the angle between sides B and C is π4pi/4, and the length of B is 13, what is the area of the triangle?

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 13, what is the area of the triangle?