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.
:
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