If a right triangle has a leg with length 12 and the hypotenuse is 16, how long is the other leg? Round to the nearest tenth if necessary
To find the length of the other leg of a right triangle, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have one leg with a length of 12 and the hypotenuse with a length of 16.
Let the other leg be represented by x.
Using the Pythagorean theorem, we have:
x^2 + 12^2 = 16^2
Simplifying the equation, we have:
x^2 + 144 = 256
Subtracting 144 from both sides, we have:
x^2 = 256 - 144
x^2 = 112
Taking the square root of both sides, we have:
x = √(112)
x ≈ 10.6
Therefore, the length of the other leg of the right triangle is approximately 10.6.