A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{3 π}{4}$ $(3pi)/4$ , 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

$17.324$ $17.324$

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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

$1/2cxxh$

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

A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/8π8(pi)/8, the angle between sides B and C is (3pi)/43π4(3pi)/4, and the length of side B is 7, what is the area of the triangle?