A triangle has sides A,B, and C. If the angle between sides A and B is (3pi)/8, the angle between sides B and C is pi/12, and the length of B is 5, what is the area of the triangle?

1 Answer
Shwetank Mauria
Apr 15, 2016

Hence area of triangle is 3.015 units

Explanation:

The length of side B is 5 and angle opposite this side is angle between sides A and C, which is not given. But as other two angles are (3pi)/8 and pi/12, this angle would be

pi-(3pi)/8-pi/12=(24pi-9pi-2pi)/24=(13pi)/24

Now for using sine formula for area of triangle given by 1/2xxabxxsintheta, we need one more side. Let us choose the side C, which is opposite the angle (3pi)/8.

Now using sine rule we have

5/sin((13pi)/24)=C/sin((3pi)/8) or C=5xxsin((3pi)/8)/sin((13pi)/24)

Hence area of triangle is 1/2xx5xx5xxsin((3pi)/8)/sin((13pi)/24)xxsin(pi/12)

= 25/2xx(0.9239xx0.2588)/0.9914=3.015 units

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