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

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

Answer: (D)

Verified step by step guidance

1. Identify the given elements in the right triangle: one leg length is 6 units, and the hypotenuse length is 10 units.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the two legs (a and b): \(c^2 = a^2 + b^2\).
3. Assign the known values to the formula: let the unknown leg be \(b\), so \$10^2 = 6^2 + b^2$.
4. Calculate the squares of the known sides: \$100 = 36 + b^2$.
5. Isolate \(b^2\) by subtracting 36 from both sides: \(b^2 = 100 - 36\), then find \(b\) by taking the square root: \(b = \sqrt{100 - 36}\).