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

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Answer 1 · 2016-12-26T10:20:52

Let

1.the angle between sides A and B opposite to side C is $gamma=pi/4$

2.the angle between sides B and C opposite to side A is $alpha=(2pi)/3$

3.the angle between sides C and A opposite to side B is $beta=pi-(2pi)/3-pi/4=pi/12$

By sine law of triangle

$C/singamma=B/sinbeta$

$=>C=(Bsingamma)/sinbeta$

Area if the triangle

$Delta=1/2BxxCsinalpha$

$=1/2B^2(sinalphaxxsingamma)/sinbeta$

$=1/2xx5^2(sin((2pi)/3)sin(pi/4))/sin(pi/12)$

$~~29.57squnit$

A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/4(pi)/4, the angle between sides B and C is (2pi)/3(2pi)/3, and the length of side B is 5, what is the area of the triangle?