Question

value: 2
find the length of the missing side using the pythagorean theorem. round to the nearest tenth if necessary.
5.5 ft
7.9 ft

a. 13.1
b. 9.6
c. 12
d. 18.2

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(a = 5.5\) ft and \(b=7.9\) ft, and we want to find \(c=x\).
\[x=\sqrt{5.5^{2}+7.9^{2}}\]

Step2: Calculate squares

First, calculate \(5.5^{2}=5.5\times5.5 = 30.25\) and \(7.9^{2}=7.9\times7.9 = 62.41\).
\[x=\sqrt{30.25 + 62.41}\]

Step3: Add values inside square - root

\[30.25+62.41 = 92.66\]
\[x=\sqrt{92.66}\]

Step4: Find square - root and round

\(\sqrt{92.66}\approx9.6\) (rounded to the nearest tenth)

Answer:

B. 9.6