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 $\frac{5 π}{24}$ $(5pi)/24$ and the angle between B and C is $\frac{3 π}{8}$ $(3pi)/8$ . What is the area of the triangle?

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Answer 1 · 2017-07-17T17:14:51

The area is $= 9.66 u^{2}$ $=9.66u^2$

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The dimensions of the triangle are

Side $a = 4$ $a=4$

Side $b = 5$ $b=5$

Angle $ˆ B = \frac{5}{24} π$ $hatB=5/24pi$

Angle $ˆ A = \frac{3}{8} π$ $hatA=3/8pi$

Therefore,

Angle $ˆ C = π - (\frac{5}{24} π + \frac{3}{8} π)$ $hatC=pi-(5/24pi+3/8pi)$

$= π - \frac{7}{12} π$ $=pi-7/12pi$

$= \frac{5}{12} π$ $=5/12pi$

The area of the triangle is

$= \frac{1}{2} \cdot a \cdot b \cdot sin ˆ C$ $=1/2*a*b*sin hatC$

$= \frac{1}{2} \cdot 4 \cdot 5 \cdot sin (\frac{5}{12} π)$ $=1/2*4*5*sin(5/12pi)$

$= 9.66 u^{2}$ $=9.66u^2$

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 5π24(5pi)/24 and the angle between B and C is 3π8 (3pi)/8. What is the area of the triangle?