Question #N838
In triangle $ABC$, angle $A$ is a right angle, and $AB = 3$ and $BC = 5$. What is the length of $AC$?
A. 2
B. 4
C. 8
D. 16
Correct Answer is: B
Triangle $ABC$ is a right triangle, so we can use the Pythagorean theorem to find the length of $AC$. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, $BC$ is the hypotenuse, so $BC^2 = AB^2 + AC^2$. Substituting the given values, we get $5^2 = 3^2 + AC^2$. This simplifies to $25 = 9 + AC^2$. Subtracting 9 from both sides, we get $16 = AC^2$. Taking the square root of both sides, we get $AC = 4$.