Question

5 find the missing side length to the nearest tenth of a foot.
14 ft
8 ft

1. find the missing side length.

6.6 mm
11.2 mm

Explanation:

Step1: (Problem 5) Define Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c=14$, $b=8$, solve for $a$.

Step2: (Problem 5) Rearrange for missing side

$a = \sqrt{c^2 - b^2}$

Step3: (Problem 5) Substitute values

$a = \sqrt{14^2 - 8^2} = \sqrt{196 - 64} = \sqrt{132}$

Step4: (Problem 5) Calculate and round

$\sqrt{132} \approx 11.5$

Step5: (Problem 6) Define Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $a=6.6$, $b=11.2$, solve for $c$.

Step6: (Problem 6) Substitute values

$c = \sqrt{6.6^2 + 11.2^2} = \sqrt{43.56 + 125.44} = \sqrt{169}$

Step7: (Problem 6) Calculate final value

$\sqrt{169} = 13$

Answer:

1. Missing side (Problem 5): 11.5 ft
2. Missing side (Problem 6): 13 mm