A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 4, respectively. The angle between A and C is $(7pi)/24$ and the angle between B and C is $(13pi)/24$ . What is the area of the triangle?

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Answer 1 · 2018-01-10T09:59:13

2

We know:
$rightarrow$ angle $A=(13pi)/24$
$rightarrow$ angle $B=(7pi)/24$

therefore we know angle $C = (4pi)/24 = pi/6$ because the angles must sum to $pi$ .

We also know:
$rightarrow$ side $a=2$
$rightarrow$ side $b=4$

So we know angle $C$ and the sides adjacent to it, $a$ and $b$ . We can find the area using:

$Area=1/2a*b*sin(C)$

$=1/2(2)(4)sin(pi/6) = 4sin(pi/6)$

since $sin(pi/6)=1/2$ , we get:

Area $= 1/2(4)=2$

A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 4, respectively. The angle between A and C is (7pi)/24(7pi)/24 and the angle between B and C is (13pi)/24 (13pi)/24. What is the area of the triangle?