A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 9, respectively. The angle between A and C is $\frac{π}{8}$ $(pi)/8$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . 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 7 and 9, respectively. The angle between A and C is $\frac{π}{8}$ $(pi)/8$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . What is the area of the triangle?

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Answer 1 · 2018-04-07T09:52:35

$since \frac{a}{sin A} \neq \frac{b}{sin B}, we can not form a triangle with the given measurements.$ $"Since " color(brown)(a / sin A != b / sin B), color(crimson)(" we can not form a triangle with the given measurements."$

Explanation:

![https://math.stackexchange.com/questions/811938/law-of-sines-and-cosines]( useruploads.socratic.org )

As per the Law of Sines, $\frac{a}{sin A} = \frac{b}{sin B}$ $a / sin A = b / sin B$

$\frac{a}{sin A} = \frac{7}{sin (\frac{π}{24})} = 53.63$ $a / sin A = 7 / sin (pi/24) = 53.63$

$\frac{b}{sin B} = \frac{9}{sin (\frac{π}{8})} = 23.52$ $b / sin B = 9 / sin (pi/8) = 23.52$

$since \frac{a}{sin A} \neq \frac{b}{sin B}, we can not form a triangle with the given measurements.$ $"Since " color(brown)(a / sin A != b / sin B), color(crimson)(" we can not form a triangle with the given measurements."$

Answer 2 · 2018-04-07T10:01:28

$Inconsistency in the given measurements according to the Greater Angle and Greater Side Theorem$ $color(purple)("Inconsistency in the given measurements according to the Greater Angle and Greater Side Theorem"$

Explanation:

![https://study.com/academy/lesson/http://inequalities-in-one-triangle.html](https://useruploads.socratic.org/WIIKmWEdRSSQY5gwG8Az_greater%20angle%20greater%20side.jpg)

$As per the Greater Angle and Greater Side Theorem'$ $"As per the Greater Angle and Greater Side Theorem'"$

$b > a, if and only if ˆ B > ˆ A$ $b > a, "if and only if " hat B > hat A$

$since ˆ B < ˆ A, though b > a, we cannot form a triangle with the given measures.$ $"Since " hat B < hat A, " though " b > a, " we cannot form a triangle with the given measures."$

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A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 9, respectively. The angle between A and C is $\frac{π}{8}$ $(pi)/8$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . 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 7 and 9, respectively. The angle between A and C is π8(pi)/8 and the angle between B and C is π24 (pi)/24. What is the area of the triangle?

2 Answers

Explanation:

Explanation:

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A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 9, respectively. The angle between A and C is $\frac{π}{8}$ $(pi)/8$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . What is the area of the triangle?