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

• A. $8$
• B. $4$
• C. $10$
• D. $7$

Answer: (A)

Verified step by step guidance

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