A triangle has sides A, B, and C. The angle between sides A and B is $pi/3$ and the angle between sides B and C is $pi/12$ . If side B has a length of 5, what is the area of the triangle?

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Answer 1 · 2016-05-19T09:06:56

Area of triangle is $2.90$

The third angle opposite sides $A$ and $C$ is

$pi-pi/3-pi/12=(12-4-1)pi/12=5pi/12$ and it has side $B=5$ opposite it.

As side $A$ has angle opposite it $pi/12$ , using sine formula, we get

$A/sin(pi/12)=B/sin((5pi)/12)$ or

$A=Bxxsin(pi/12)/sin((5pi)/12)=5xx0.2588/0.9659=1.34$

Hence area of triangle is $1/2xx5xx1.34xxsin(pi/3)$

= $1/2xx5xx1.34xx0.866=2.90$

A triangle has sides A, B, and C. The angle between sides A and B is pi/3pi/3 and the angle between sides B and C is pi/12pi/12. If side B has a length of 5, what is the area of the triangle?