What is the length of the missing leg of a right triangle whose hypotenuse is 10 and has one leg that measures 5 square root 3?

To find the length of the missing leg of the right triangle, we can use the Pythagorean theorem, which states ( a^2 + b^2 = c^2 ), where ( c ) is the hypotenuse. Given that the hypotenuse ( c = 10 ) and one leg ( a = 5\sqrt{3} ), we can set up the equation:

[ (5\sqrt{3})^2 + b^2 = 10^2 ]

Calculating, we find ( 75 + b^2 = 100 ), leading to ( b^2 = 25 ). Thus, the length of the missing leg ( b ) is ( 5 ).