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: HW Triangles Question 5, 10.2.25 HW Score: 30\%, 30 of 100 points Points: 0 of 10 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 triangle, the hypotenuse is 16 cm, one leg is 12 cm, and the other leg is 'a'. Thus, we can write the equation:

a² + 12² = 16²

Step 2: Solve for 'a'

Simplify and solve the equation for 'a': a² + 144 = 256 a² = 256 - 144 a² = 112 a = √112 a ≈ 10.583

Step 3: Round to one decimal place

Rounding to one decimal place, we get:

a ≈ 10.6