A triangle has vertices A, B, and C. Vertex A has an angle of $pi/12$ , vertex B has an angle of $pi/6$ , and the triangle's area is $4$ . What is the area of the triangle's incircle?

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Answer 1 · 2016-10-01T19:22:49

$pir² ~~ 1.07$

Given:

$Delta = 4$ where $Delta$ is the area of the triangle.
$A = pi/12$
$B = pi/6$

We can compute the measure of angle C:

$C = pi - A - B = 3pi/4$

Using a equation from the source

$Delta = r²(cot(A/2) + cot(B/2) + cot(C/2))$

The area of the incircle is $pir²$

$pir² = piDelta/(cot(A/2) + cot(B/2) + cot(C/2))$

$pir² ~~ 1.07$

A triangle has vertices A, B, and C. Vertex A has an angle of pi/12 pi/12 , vertex B has an angle of pi/6 pi/6 , and the triangle's area is 4 4 . What is the area of the triangle's incircle?