To find the radius of inscribed circle in isosceles triangle:
1) Find the leg of the triangle, using the Pythagorean Theorem:
c² = a² + b² , where c is the missing leg
c² = 15² + (16/2)²
c² = 225 + 64
c² = 289
[tex] \sqrt{c ^{2} } = \sqrt{289} [/tex]
c = 17
2) Find the radius:
leg = 17; base = 16
radius = [tex] \frac{base}{2} \sqrt{} \frac{2(leg)-base}{2(leg)+base} [/tex]
radius = [tex] \frac{16}{2} \sqrt{ \frac{2(17)-16}{2(17)+16} } [/tex]
radius = [tex]8 \sqrt{ \frac{34-16}{34+16} } [/tex]
radius = [tex]8 \sqrt{ \frac{18}{50} } = 8 \sqrt{ \frac{9}{25} } [/tex]
radius = 8 (³/₅)
radius = 24/5
radius = 4.8 inches
