A triangle has sides A,B, and C. If the angle between sides A and B is $(pi)/12$ , the angle between sides B and C is $pi/3$ , and the length of B is 7, what is the area of the triangle?

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Answer 1 · 2016-12-06T15:51:51

Let

$alpha->"angle between B and C"=pi/3$

$beta->"angle between A and C"=pi-(pi/3+pi/12)=(7pi)/12$

$gamma->"angle between B and A"=pi/12$

$"side " B=7$

By properties of triangle

$C/singamma=B/sinbeta$

$C=(Bsingamma)/sinbeta$

Now area of the triangle

$Delta=1/2BCsinalpha$

$=>Delta=1/2xxBxx(Bsingamma)/sinbetaxxsinalpha$

$=1/2xx7^2xx(sin(pi/12)sin(pi/3))/sin((7pi)/12)$

$~~5.685" squnit"$

A triangle has sides A,B, and C. If the angle between sides A and B is (pi)/12(pi)/12, the angle between sides B and C is pi/3pi/3, and the length of B is 7, what is the area of the triangle?