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

Algebra ->  Circles -> 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      Log On


   

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) About Me  (Show Source):
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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 =+pi%2Ar%5E2+=+pi%2A5%5E2

P(Pt in circle will land in rtΔ) = 24/25*3.14 = .3057 or 30.6%

Answer by jerryguo41(197) About Me  (Show Source):
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Circle diameter of 10
Area of Circle is
A=πr^2
A=π10^2
A=100%26%23960%3B
Area of Triangle is Hight*Base/2
Using Pythagorean THM
A%5E2%2BB%5E2=C%5E2
8%5E2%2BB%5E2=10%5E2
64%2BB%5E2=100
B%5E2=+36
B=6
Area of Triangle
Hight%2ABase%2F2
%288%2A6%29%2F2
48%2F2
24
% landing in triangle
Area of Triangle/Area of Circle
24/100π = 24/314.2 = 0.08%

Answer by richard1234(7193) About Me  (Show Source):
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Jerry, the radius is 5 and not 10. The area of the circle is pi*(5^2) = 25pi.