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

1 Answer
Alan P.
Dec 23, 2015

Area = 9/(4(2+sqrt(3)))

Explanation:

(see diagram)
enter image source here

By Half Angle Formula for tan
color(white)("XXX")tan(pi/12) = sin(pi/6)/(1+cos(pi/6))
using standard values for sin and cos
color(white)("XXX")tan(pi/12)= 1/(2+sqrt(3))

The height of the triangle is
color(white)("XXX")h=3/2 xx tan(pi/12)

and the area is
color(white)("XXX")("base " xx " height")/2

color(white)("XXX")=(3xx3/2xxtan(pi/2))/2

color(white)("XXX")=9/4xx1/(2+sqrt(3))

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