A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 23, 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 $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 23, what is the area of the triangle?

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Answer 1 · 2017-05-05T16:33:12

This is a right triangle with hypotenuse $B = 23$ $B = 23$

Explanation:

The area is

$\frac{1}{2} (23 sin (\frac{π}{12})) (23 cos (\frac{π}{12})) = \frac{529}{2} (sin (\frac{π}{12}) cos (\frac{π}{12}))$ $1/2(23sin(pi/12))(23cos(pi/12)) = 529/2 (sin(pi/12)cos(pi/12))$

$= \frac{529}{2} (\frac{1}{2} sin (\frac{2 π}{12}))$ $= 529/2(1/2sin((2pi)/12))$

$= \frac{529}{4} (sin (\frac{π}{6}))$ $= 529/4(sin(pi/6))$

$= \frac{529}{8}$ $= 529/8$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 23, 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 5π12(5pi)/12 and the angle between sides B and C is π12pi/12. If side B has a length of 23, 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 $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 23, what is the area of the triangle?