use the pythagorean theorem to find the length of the hypotenuse of each right triangle. the lengths of the legs are given. round answer to the nearest tenth. 9) 16 in., 30 in. 10) 8 ft., 15 ft. 11) 1 ft., 2 ft. 12) 5 in., 5 in. 13) find the distance across the lake. 14) how far is the balloon from the weather station? 15) how long is the ladder?

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Accepted Answer

# Explanation:
## Step1: Recall the Pythagorean Theorem
The Pythagorean Theorem is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the lengths of the legs of a right - triangle and $c$ is the length of the hypotenuse.
## Step2: Substitute the values for problem 9
For problem 9, $a = 16$ in and $b=30$ in. Then $c^{2}=16^{2}+30^{2}$.
$$
\begin{align*}
c^{2}&=256 + 900\
c^{2}&=1156\
c&=\sqrt{1156}\
c& = 34
\end{align*}
$$
## Step3: Substitute the values for problem 10
For problem 10, $a = 8$ ft and $b = 15$ ft. Then $c^{2}=8^{2}+15^{2}$.
$$
\begin{align*}
c^{2}&=64+225\
c^{2}&=289\
c&=\sqrt{289}\
c&=17
\end{align*}
$$
## Step4: Substitute the values for problem 11
For problem 11, $a = 1$ ft and $b = 2$ ft. Then $c^{2}=1^{2}+2^{2}$.
$$
\begin{align*}
c^{2}&=1 + 4\
c^{2}&=5\
c&=\sqrt{5}\approx2.2
\end{align*}
$$
## Step5: Substitute the values for problem 12
For problem 12, $a = 5$ in and $b = 5$ in. Then $c^{2}=5^{2}+5^{2}$.
$$
\begin{align*}
c^{2}&=25+25\
c^{2}&=50\
c&=\sqrt{50}\approx7.1
\end{align*}
$$
## Step6: Solve problem 13
For problem 13, $a = 8$ ft and $b = 15$ ft. Then $c^{2}=8^{2}+15^{2}$.
$$
\begin{align*}
c^{2}&=64 + 225\
c^{2}&=289\
c&=\sqrt{289}\
c&=17\text{ ft}
\end{align*}
$$
## Step7: Solve problem 14
For problem 14, $a = 6$ km and $b = 5$ km. Then $c^{2}=6^{2}+5^{2}$.
$$
\begin{align*}
c^{2}&=36+25\
c^{2}&=61\
c&=\sqrt{61}\approx7.8\text{ km}
\end{align*}
$$
## Step8: Solve problem 15
For problem 15, $a = 6$ ft and $b = 12$ ft. Then $c^{2}=6^{2}+12^{2}$.
$$
\begin{align*}
c^{2}&=36+144\
c^{2}&=180\
c&=\sqrt{180}\approx13.4\text{ ft}
\end{align*}
$$

# Answer:
9) $34$ in.
10) $17$ ft.
11) $\approx2.2$ ft.
12) $\approx7.1$ in.
13) $17$ ft.
14) $\approx7.8$ km.
15) $\approx13.4$ ft.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the Pythagorean Theorem

Step2: Substitute the values for problem 9

Step3: Substitute the values for problem 10

Step4: Substitute the values for problem 11

Step5: Substitute the values for problem 12

Step6: Solve problem 13

Step7: Solve problem 14

Step8: Solve problem 15

Answer: