A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 4, respectively. The angle between A and C is $(17pi)/24$ and the angle between B and C is $(pi)24$ . What is the area of the triangle?

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Answer 1 · 2018-07-16T10:58:15

$5\sqrt2\ \text{unit}^2$

We know that the sum of all interior angles of a triangle is always $\pi$ then the angle between sides A & B is given as

$\pi-\text{angle between sides A & C}-\text{angle between sides B & C}$

$=\pi-{17\pi}/24-{\pi}/24$

$={6\pi}/24$

$=\pi/4$

hence, the area of given triangle having sides $A=5$ , $B=4$ & their included angle $\angle C=\pi/4$ is given as follows

$1/2AB\sin\angle C$

$=1/2(5)(4)\sin(\pi/4)$

$=10\cdot 1/\sqrt2$

$=5\sqrt2\ \text{unit}^2$

A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 4, respectively. The angle between A and C is (17pi)/24(17pi)/24 and the angle between B and C is (pi)24 (pi)24. What is the area of the triangle?