Calculate the missing side of the triangle below.

• A. 9
• B. 25
• C. 19$$
• D. 15

Answer: (D)

Verified step by step guidance

1. Identify the type of triangle: The triangle is a right triangle, as indicated by the right angle symbol.
2. Apply the Pythagorean theorem: 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. The formula is: \( c^2 = a^2 + b^2 \), where \( c \) is the hypotenuse.
3. Substitute the known values into the Pythagorean theorem: Here, the hypotenuse \( c = 17 \), and one of the legs \( a = 8 \). The other leg \( b = x \) is the unknown side we need to find. Substitute these into the equation: \( 17^2 = 8^2 + x^2 \).
4. Calculate the squares of the known sides: Compute \( 17^2 \) and \( 8^2 \). This gives \( 289 = 64 + x^2 \).
5. Solve for \( x^2 \): Subtract 64 from both sides to isolate \( x^2 \): \( x^2 = 289 - 64 \). Then, take the square root of both sides to solve for \( x \).