A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is $\frac{5 π}{8}$ $(5pi)/8$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?

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A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is $\frac{5 π}{8}$ $(5pi)/8$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?

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Answer 1 · 2018-03-27T11:42:40

$A_{t} = (\frac{1}{2}) a b sin C = 8.75 sq units$ $color(purple)(A_t = (1/2) a b sin C = 8.75 " sq units"$

Explanation:

$a = 5, b = 7, ˆ A = \frac{5 π}{24}, ˆ B = \frac{5 π}{8}$ $a = 5, b = 7, hat A = (5pi)/24, hat B = (5pi)/8$

To find the area of the triangle $A_{t}$ $A_t$

$ˆ C = π - \frac{5 π}{24} - \frac{5 π}{8} = \frac{π}{6}$ $hat C = pi - (5pi)/24 - (5pi)/8 = pi/6$

$A_{t} = (\frac{1}{2}) a b sin C = (\frac{1}{2}) \cdot 5 \cdot 7 \cdot sin (\frac{π}{6}) = 8.75$ $color(purple)(A_t = (1/2) a b sin C = (1/2) * 5 * 7 * sin (pi/6) = 8.75$

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A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is $\frac{5 π}{8}$ $(5pi)/8$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?

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A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is 5π8(5pi)/8 and the angle between B and C is 5π24 (5pi)/24. What is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is $\frac{5 π}{8}$ $(5pi)/8$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?