SOLUTION: The hypotenuse of a right triangle is StartRoot 19 inches EndRoot and one leg measures 3 in. Find the length of the other leg.

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Question 1097746: The hypotenuse of a right triangle is StartRoot 19 inches EndRoot and one leg measures 3 in. Find the length of the other leg.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
we have a hypotenuse as sqrt(19) and one leg of 3.

by pythagorus, c^2 = a^2 + b^2, where:

c is the hypotenuse of the right triangle.
a and b are legs of the right triangle.

therefore sqrt(19)^2 = 3^2 + x^2, where x represents one of the legs.

it doesn't matter what name you use as long as you know what the name represents.

simplify the equation to get 19 = 9 + x^2

solve for x^2 to get x^2 = 10

solve for x to get x = sqrt(10).

one leg is 3
one leg is sqrt(10).
the hypotenuse is sqrt(19).

c^2 = a^2 + b^2 becomes sqrt(19)^2 = 3^2 + sqrt(10)^2 which becomes 19 = 9 + 10 which becomes 19 = 19 which confirms the value of the other leg is sqrt(10).