A triangle has sides A,B, and C. If the angle between sides A and B is $pi/4$ , the angle between sides B and C is $pi/12$ , and the length of B is 7, what is the area of the triangle?

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Answer 1 · 2018-07-04T21:03:22

$5.177459202\ \text{unit}^2$

The third angle between sides A & C in given triangle is given as

$=\pi-\pi/4-\pi/12={2\pi}/3$

Applying Sine rule in given triangle as follows

$\frac{B}{\sin({2\pi}/3)}=\frac{C}{\sin(\pi/4)}$

$\frac{7}{\sqrt3/2}=\frac{C}{1/\sqrt2}$

$C=7\sqrt{2/3}$

Now, the area of given triangle with two sides $B=7$ & $C=7\sqrt{2/3}$ including an angle $\pi/12$ is

$=1/2BC\sin(\pi/12)$

$=1/2(7)(7\sqrt{2/3})\frac{\sqrt3-1}{2\sqrt2}$

$=49/4(1-1/\sqrt3)$

$=5.177459202\ \text{unit}^2$

A triangle has sides A,B, and C. If the angle between sides A and B is pi/4pi/4, the angle between sides B and C is pi/12pi/12, and the length of B is 7, what is the area of the triangle?