A triangle has vertices A, B, and C. Vertex A has an angle of $pi/2$ , vertex B has an angle of $( pi)/3$ , and the triangle's area is $4$ . What is the area of the triangle's incircle?

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Answer 1 · 2018-04-15T12:30:13

$0.42 units^2$

The formula for the radius, $r$ of incircle is given by $r=A_t/s$ , where $A_t=$ Area of the Triangle, and $s=$ semi-perimeter.

$triangleABC$ is a right-angled triangle since vertex A $=pi/2$ .

Since vertex B $=pi/3$ , using trigonometric ratios, $a=2, b=sqrt(3), c=1$ .

$r=A_t/s=(1/2(1)(sqrt3))/(1/2(1+2+sqrt3))=sqrt(3)/(3+sqrt(3))=(sqrt3-1)/2$

Hence, area of incircle $=pir^2=pi((sqrt3-1)/2)^2approx0.42 units^2$

A triangle has vertices A, B, and C. Vertex A has an angle of pi/2 pi/2 , vertex B has an angle of ( pi)/3 ( pi)/3 , and the triangle's area is 4 4 . What is the area of the triangle's incircle?