Right triangle

A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle?

Correct result:

h =  4.8 cm

Solution:

a=6 cm R=5 cm  c=2⋅ R=2⋅ 5=10 cm  b=c2−a2=102−62=8 cm  S=a⋅ b2=6⋅ 82=24 cm2 S=c⋅ h2  h=2⋅ S/c=2⋅ 24/10=245=245 cm=4.8 cm

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