A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 5, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . 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 1 and 5, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . What is the area of the triangle?

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Answer 1 · 2016-03-03T07:30:29

$5 \frac{\sqrt{3} + 1}{4 \sqrt{2}}$ $5(sqrt3+1)/(4sqrt2)$ areal units = 0.9859 areal units, nearly..

Explanation:

Using the sum of the angles is $π$ $pi$ , the third angle between side A and B is $7 \frac{π}{12}$ $7pi/12$ .
The area is $\frac{1}{2} A B sin (∠ b e t w e e n A and B)$ $1/2ABsin(angle between A and B)$
$sin (7 \frac{π}{12}) = sin (\frac{π}{3} + \frac{π}{4})$ $sin(7pi/12) = sin(pi/3+pi/4)$
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A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 5, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . 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 1 and 5, respectively. The angle between A and C is 7π24(7pi)/24 and the angle between B and C is π8 (pi)/8. 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 1 and 5, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . What is the area of the triangle?