A triangle has sides A, B, and C. The angle between sides A and B is (pi)/6 and the angle between sides B and C is pi/6. If side B has a length of 5, what is the area of the triangle?

1 Answer
Leland Adriano Alejandro
Jan 27, 2016

Area=(25sqrt3)/12=3.60844 square units

Explanation:

The triangle is isosceles. The base angles A=pi/6=30^@ and B=pi/6=30^@. We can readily see that 1/2 of the base b equal 5/2. Use 5/2 to compute side c.

Cos (pi/6)=(5/2)/c

c=(5/2)/cos (pi/6)=(5/2)/(sqrt(3)/2)=5/sqrt3=(5sqrt3)/3

Compute the Area now using the formula for two sides and an included angle

Area=1/2*b*c*sin A

Area=1/2*5*(5sqrt3)/3*sin (pi/6)

Area=1/2*5*(5sqrt3)/3*1/2

Area=(25sqrt3)/12=3.60844 square units

Have a nice day!!! from the Philippines

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