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#