Right triangle ABC has one leg of length 6 cm, one leg of length 10 cm, and a right angle at A. A square has one side on the hypotenuse of triangle ABC and a vertex on each of the two legs of triangle ABC. What is the length of one side of the square in cm? Express your answer as a common fraction.
+1486 Right triangle ABC has one leg of length 6 cm, one leg of length 10 cm, and a right angle at A. A square has one side on the hypotenuse of triangle ABC and a vertex on each of the two legs of triangle ABC. What is the length of one side of the square in cm? Express your answer as a common fraction.
Let the side of the square be x
x / tan(B) + x + x / tan(C) = sqrt(62 + 102)
x = 3.56997
