A right triangle has a hypotenuse of length $10$ units and one leg of length $6$ units. What is the length of the other leg of the triangle?

• A. $\sqrt{36}$ units
• B. $\sqrt{100}$ units
• C. $\sqrt{64}$ units
• D. $\sqrt{16}$ units

Answer: (C)

Verified step by step guidance

1. Identify the given elements of the right triangle: the hypotenuse length \(c = 10\) units and one leg length \(a = 6\) units.
2. Recall the Pythagorean theorem, which relates the sides of a right triangle: \(a^2 + b^2 = c^2\), where \(b\) is the length of the other leg.
3. Substitute the known values into the Pythagorean theorem: \$6^2 + b^2 = 10^2$.
4. Calculate the squares of the known sides: \$36 + b^2 = 100$.
5. Isolate \(b^2\) by subtracting 36 from both sides: \(b^2 = 100 - 36\), then find \(b\) by taking the square root: \(b = \sqrt{64}\).