Given a right triangle with one leg measuring $5$ units and the hypotenuse measuring $8.6$ units, which of the following is the length of the unknown side rounded to the nearest whole number?

• A. $8$ units
• B. $9$ units
• C. $7$ units
• D. $6$ units

Answer: (C)

Verified step by step guidance

1. Identify the given elements of the right triangle: one leg is 5 units, and the hypotenuse is 8.6 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 \$8.6^2 = 5^2 + b^2$.
4. Rearrange the equation to solve for \(b^2\): \(b^2 = 8.6^2 - 5^2\).
5. Take the square root of both sides to find \(b\): \(b = \sqrt{8.6^2 - 5^2}\), then round the result to the nearest whole number.