SOLUTION: A right triangle is inscribed a circle with a diameter of 10. The height of the triangle is 8 and its hypotenuse has a length of 10. If you choose a point in the given circle, find

Question 388933: A right triangle is inscribed a circle with a diameter of 10. The height of the triangle is 8 and its hypotenuse has a length of 10. If you choose a point in the given circle, find the probability it will land in the shaded region (aka, the right triangle). (answer in % form and rounded to the nearest tenth)
Found 3 solutions by ewatrrr, jerryguo41, richard1234:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi

Applying pythagorean Theorem to determine length of base of the rtΔ
10^2 = b^2 + 8^2
100 - 64 = b^2
36 = b^2
6 = b (tossing out neg solution)
P(Pt in circle will land in rtΔ) = Area rtΔ/Area circle
Area rtΔ = (1/2) b*h
Area rtΔ = 24
Area circle =
P(Pt in circle will land in rtΔ) = 24/25*3.14 = .3057 or 30.6%

Answer by jerryguo41(197)   (Show Source): You can put this solution on YOUR website!
Circle diameter of 10
Area of Circle is
A=πr^2
A=π10^2

Area of Triangle is Hight*Base/2
Using Pythagorean THM

Area of Triangle

% landing in triangle
Area of Triangle/Area of Circle
24/100π = 24/314.2 = 0.08%

Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
Jerry, the radius is 5 and not 10. The area of the circle is pi*(5^2) = 25pi.
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