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 #(2pi)/3#, and the length of side B is 5, what is the area of the triangle?

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Answer 1 · 2017-07-14T07:10:40

The area of the triangle is #=9.52u^2#

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The angles are

#hat(C)=1/8pi#

#hat(A)=2/3pi#

This is an isoceles triangle.

#hat(B)=pi-(1/8pi+2/3pi)=5/24pi#

#b=5#

We apply the sine rule to the triangle

#a/sin(hat(A))=b/sin(hat(B))#

#a/sin(2/3pi)=5/sin(5/24pi)#

#a=5*sin(2/3pi)/sin(5/24pi)=7.11#

The area of the triangle is

#=1/2*a*bsin(hat(C))#

#=1/2*7.11*7*sin(1/8pi)#

#=9.52#