A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{3 π}{8}$ $(3pi)/8$ . What is the area of the triangle?

Question

1570 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-17T12:02:22

We can not form a triangle

$a = 4, b = 5, ˆ A = \frac{3 π}{8}, ˆ B = \frac{13 π}{24}$ $a = 4, b = 5, hatA = (3pi)/8, hatB = (13pi)/24$

$ˆ C = π - \frac{3 π}{8} - \frac{13 π}{24} = \frac{π}{12}$ $hatC = pi - (3pi)/8 - (13pi)/24 = pi/12$

enter image source here

$\frac{a}{sin A} = \frac{4}{sin (\frac{3 π}{8})} = 4.3296$ $a/sin A = 4 / sin ((3pi)/8 )= 4.3296$

$\frac{b}{sin B} = \frac{5}{sin (\frac{13 π}{24})} = 5.0431$ $b / sin B = 5 / sin ((13pi)/24) = 5.0431$

Since $\frac{a}{sin A} \neq \frac{b}{sin B}$ $a / sin A != b / sin B$ , we cannot form a triangle.

A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is 13π24(13pi)/24 and the angle between B and C is 3π8 (3pi)/8. What is the area of the triangle?