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 3, what is the area of the triangle?

1 Answer
Alan P.
Dec 6, 2016

"Area"_triangle=color(green)((9sqrt(3))/4)

Explanation:

As can be seen from the image below, the given triangle can be split into 2 triangles with angles: pi/6, pi/3, and pi/2
This is the ratios for one of that standard trigonometric triangles
we can see that the height of the original triangle must be color(red)(3/2 *sqrt(3))

enter image source here
and the triangle's area will be:
color(white)("XXX")1/2 * b * h = 1/2 xx 3 xx((3sqrt(3))/2)=(9sqrt(3))/4

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