In right triangle $ABC$, angle $B$ is the right angle. If $AB$ = $7$ units and $BC$ = $9$ units, what is the length of line segment $AC$?

• A. $18$
• B. $16$
• C. $14$
• D. $11$

Answer: (D)

Verified step by step guidance

1. Identify the right triangle ABC where angle B is the right angle, meaning side AC is the hypotenuse opposite the right angle.
2. Recall the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (AC) equals the sum of the squares of the other two sides: \(AC^2 = AB^2 + BC^2\).
3. Substitute the given side lengths into the Pythagorean theorem: \(AC^2 = 7^2 + 9^2\).
4. Calculate the squares of the given sides: \$7^2 = 49\( and \)9^2 = 81\(, so \)AC^2 = 49 + 81$.
5. Add the values and then take the square root of the sum to find the length of AC: \(AC = \sqrt{49 + 81}\).