A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/8, the angle between sides B and C is (5pi)/12, and the length of B is 1, what is the area of the triangle?

1 Answer
bp
Feb 25, 2017

1.23

Explanation:

For sake of easy calculations, the angle measures in degrees would be angle A = 75^o, angle B=22.5^o and angle C= 82.5^0 as shown in the figure below

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Now using sin A/a= sin B/b= sin C /c, it would be

sin 75 /a= sin 22.5/1= sin 82.5/c

Thus a= sin 75/sin 22.5=2.52; c= sin 82.5/ sin22.5= 2.59

Now for using Heron formula for the area of a triangle, s=(2.52+1+2.59)/2= 6.11/2= 3.05

(s-a)= 0.53, (s-b)= 2.05, and (s-c)= 0.46

Area of Triangle would be= sqrt(3.05(0.53)(2.05)(0.46))=1.23

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