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 #(3pi)/4#, and the length of side B is 7, what is the area of the triangle?

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Answer 1 · 2018-02-09T18:06:04

#17.324#

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From the diagram:

#bbtheta=pi-((3pi)/4+pi/8)=pi/8#

#bbalpha=pi-(3pi)/4=pi/4#

Using The Sine Rule

#bb(SinA/a=SinB/b=SinC/c#

We only need to find side #bbc#

We know angle B and side b, so:

#sin(pi/8)/7=sin(pi/8)/c=>c=(7sin(pi/8))/sin(pi/8)=7#

From diagram:

#bb(h)=7sin(pi/4)#

Area of triangle is:

#bb(1/2)#base x height

#1/2cxxh#

#1/2(7)*7sin(pi/4)=(49sqrt(2))/4=17.324#