13)
$(2)^2 + (5)^2 = (c)^2$
(right triangle with legs 5 and 2, hypotenuse c)
15)
(right triangle with hypotenuse 7.4, leg 3.6, and other leg a, also a segment r inside)

Question

Accepted Answer

# Explanation:
## Step1: Solve for $ C $ in problem 13
We use the Pythagorean theorem $ a^2 + b^2 = c^2 $, where $ a = 2 $, $ b = 5 $, and $ c = C $.
$$
\begin{align*}
2^2 + 5^2 &= C^2 \
4 + 25 &= C^2 \
29 &= C^2 \
C &= \sqrt{29} \approx 5.385
\end{align*}
$$
## Step2: Solve for $ a $ in problem 15
Using the Pythagorean theorem $ a^2 + b^2 = c^2 $, where $ b = 3.6 $, $ c = 7.4 $, and we solve for $ a $.
$$
\begin{align*}
a^2 + 3.6^2 &= 7.4^2 \
a^2 + 12.96 &= 54.76 \
a^2 &= 54.76 - 12.96 \
a^2 &= 41.8 \
a &= \sqrt{41.8} \approx 6.465
\end{align*}
$$
# Answer:
For problem 13: $ C = \sqrt{29} \approx 5.39 $ (rounded to two decimal places)
For problem 15: $ a = \sqrt{41.8} \approx 6.47 $ (rounded to two decimal places)

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QUESTION IMAGE

Question

Explanation:

Step1: Solve for \( C \) in problem 13

Step2: Solve for \( a \) in problem 15

Answer: