Questions: Solve for the missing side length. 3 sqrt(61) 9 sqrt(61) sqrt(549) 3 sqrt(11)

Transcript text: Solve for the missing side length. $3 \sqrt{61}$ $9 \sqrt{61}$ $\sqrt{549}$ $3 \sqrt{11}$

Solution

Solution Steps

Step 1: Apply the Pythagorean theorem

The Pythagorean theorem states that in a right-angled 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, z is the hypotenuse, and the other two sides have lengths 15 and 18. Therefore:

z² = 15² + 18²

Step 2: Calculate the squares

15² = 225 18² = 324

Step 3: Sum the squares and find the square root

z² = 225 + 324 z² = 549 z = √549