What is the radius of the circle inscribed in triangle ABC$ if AB = 15, AC = 41, and BC = \(42\)?
+580 The Radius of a circle inscribed in a triangle can be found using the formula Area of triangle/semi perimeter of the triangle:
We can find the semi perimeter by adding all the known sides and dividing by 2.
That would be (15+41+42)/2 = 98/2 = 49
We can find the area of the triangle using the heron's formula:
sqrt(49(49-15)(49-41)(49-42))
= 28*sqrt(119) = approx 305.44393
Substituting that in the Area of triangle/semi perimeter of the triangle formula:
28*sqrt(119)/49
= (4sqrt(17))/sqrt(7) or approx. 6.23354 units
If you want, rationalise the radical. Its up to you 
-Vinculum
+580 The Radius of a circle inscribed in a triangle can be found using the formula Area of triangle/semi perimeter of the triangle:
We can find the semi perimeter by adding all the known sides and dividing by 2.
That would be (15+41+42)/2 = 98/2 = 49
We can find the area of the triangle using the heron's formula:
sqrt(49(49-15)(49-41)(49-42))
= 28*sqrt(119) = approx 305.44393
Substituting that in the Area of triangle/semi perimeter of the triangle formula:
28*sqrt(119)/49
= (4sqrt(17))/sqrt(7) or approx. 6.23354 units
If you want, rationalise the radical. Its up to you
-Vinculum
