Question

find each missing length to the nearest tenth.
7)
4
8
8)
6
3
9)
7
10
10)
3
7
11)
7
2
12)
2
6
(handwritten: a² + b² = c² for each problem, and for problem 8, 56.25 = 56.25 with yes circled)

Explanation:

Problem 7:

Step1: Identify sides (a=4, b=?, c=8)

We use the Pythagorean theorem \(a^2 + b^2 = c^2\). Rearranging for \(b\): \(b = \sqrt{c^2 - a^2}\)

Step2: Substitute values (\(a = 4\), \(c = 8\))

\(b = \sqrt{8^2 - 4^2} = \sqrt{64 - 16} = \sqrt{48} \approx 6.9\)

Step1: Identify sides (a=6, b=3, c=?)

Use \(a^2 + b^2 = c^2\)

Step2: Substitute values (\(a = 6\), \(b = 3\))

\(c = \sqrt{6^2 + 3^2} = \sqrt{36 + 9} = \sqrt{45} \approx 6.7\)

Step1: Identify sides (a=7, b=10, c=?)

Use \(a^2 + b^2 = c^2\)

Step2: Substitute values (\(a = 7\), \(b = 10\))

\(c = \sqrt{7^2 + 10^2} = \sqrt{49 + 100} = \sqrt{149} \approx 12.2\)

Answer:

6.9

Problem 8: