SOLUTION: A right triangle is inscribed in a circle of radius 7.5 cm. One of its sides is 15 cm long and its area is 54 square cm. Find the length of one side of the triangle.

Question 705207: A right triangle is inscribed in a circle of radius 7.5 cm. One of its sides is 15 cm long and its area is 54 square cm. Find the length of one side of the triangle.
Found 2 solutions by ankor@dixie-net.com, KMST:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A right triangle is inscribed in a circle of radius 7.5 cm.
One of its sides is 15 cm long and its area is 54 square cm.
Find the length of one side of the triangle.
:
The 15 cm side is the diameter (2*7.5), the longest possible side, therefore
it has to be the hypotenuse
Let other two sides = a & b
:
Area of the right triangle: .5(a*b) = 54
a * b = 54*2
a * b = 108
b = 108/a
:
Pythagoras
a^2 + b^2 = 15^2
a^2 + b^2 = 225
replace b with 108/a
a^2 + (108/a)^2 = 225
a^2 + (11664/a^2) = 225
multiply by a^2
a^4 + 11664 = 225a^2
a^4 - 225a^2 + 11664 = 0
Solve this on your graphing calc
Two solutions
a = 9, then b = 12
a = 12 then b = 9
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
NOTE:
If you have studied about angles inscribed in a circle, you would know that a right angle subtends a arc (and the diameter), so the problem did not have to tell you that one side measures 15 cm, because you knew that the diameter was 15 cm.
That was redundant information, given to make the problem easier.
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