A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 1, 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 $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 1, what is the area of the triangle?

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Answer 1 · 2016-02-23T07:02:01

( $\sqrt{}$ $sqrt$ 2 $-$ $-$ 1) / (2 $\sqrt{}$ $sqrt$ 2).

Explanation:

Angle between B and C is 5 $π$ $pi$ /8 .
Use sides are proportional to sines of opposite angles and area to find C = tan $π$ $pi$ /8.
Area = 1/2 B.C. sin $π$ $pi$ 4.= sin $π$ $pi$ /8 .sin $π$ $pi$ /8 = ( 1 $-$ $-$ cos $π$ $pi$ /4)/2

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 1, 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 π8(pi)/8, the angle between sides B and C is π4pi/4, and the length of B is 1, 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 $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 1, what is the area of the triangle?