A triangle has sides A, B, and C. The angle between sides A and B is (2pi)/3 and the angle between sides B and C is pi/12. If side B has a length of 6, what is the area of the triangle?

1 Answer
Leland Adriano Alejandro
Jan 27, 2016

Area=5.70576 square units

Explanation:

To compute for the Area by using the given, there are several ways to do it.
I will present 2 solutions.
1st solution: Area = 1/2*b*h
Compute height h first. The altitude from angle B to side b:

Given angle A=pi/12 and angle C=(2pi)/3 and side b=6

h=b/(cot A+cot C)

h=6/(cot (pi/12)+cot ((2pi)/3))

h=1.90192

Compute Area:

Area=1/2*b*h=(1/2)(6)(1.90192)

Area=5.70576 square units

2nd solution:
If there are 2 sides and an included angle then, the area is determined.
Compute Angle B then apply sine law to compute side c
So that , sides b, c, and angle A area available.

Compute angle B:

B=pi-A-C=pi-pi/12-(2pi)/3=pi/4

Compute side c using Sine Law:

c=(b*sin C)/sin B=(6*sin ((2pi)/3))/sin (pi/4)

c=7.34847

Compute the Area:

Area = 1/2*b*c*sin A=1/2(6)(7.34847)sin (pi/12)

Area=5.70576 square units

Have a nice day!!! from the Philippines..

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