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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