A triangle has sides A, B, and C. The angle between sides A and B is $(5pi)/12$ and the angle between sides B and C is $pi/12$ . If side B has a length of 16, what is the area of the triangle?

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Answer 1 · 2017-06-30T07:02:50

The area of the triangle is $=32u^2$

The angle between side $A$ and $C$ is

$=pi-(5/12pi+1/12pi)=6/12pi=1/2pi$

This is a right angle triangle.

$sin(1/2pi)=1$

We apply the sine rule

$16/sin(1/2pi)=A/sin(1/12pi)$

$A=16sin(1/12pi)$

$16/1=C/sin(5/12pi)$

$C=16sin(5/12pi)$

The area of the triangle is

$=1/2ACsin(1/2pi)=1/2*16sin(1/12pi)*16sin(5/12pi)$

$=128*0.25$

$=32$

A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/12(5pi)/12 and the angle between sides B and C is pi/12pi/12. If side B has a length of 16, what is the area of the triangle?