Questions: Use the Pythagorean Theorem to find the missing length in the right triangle. The missing length is (Round to one decimal place as needed.)

Use the Pythagorean Theorem to find the missing length in the right triangle.

The missing length is (Round to one decimal place as needed.)

Transcript text: Use the Pythagorean Theorem to find the missing length in the right triangle. The missing length is $\square$ $\square$ (Round to one decimal place as needed.)

Solution

Solution Steps

Step 1: Apply the Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is 28 cm, one side is 11 cm, and the other side is 'a'. So, we have:

a² + 11² = 28²

Step 2: Simplify the equation

a² + 121 = 784

Step 3: Solve for 'a'

Subtract 121 from both sides of the equation:

a² = 784 - 121 a² = 663

Now, take the square root of both sides:

a = √663 a ≈ 25.7