Question

find the missing side length (include units). round to the nearest hundredth, if necessary. 12.9 mi 7.3 mi x
find the missing side length (include units). round to the nearest hundredth, if necessary. 35 mi x 12 mi

Explanation:

Step1: Apply Pythagorean theorem for first triangle

For a right - triangle with sides \(a = 7.3\) mi, \(b = 12.9\) mi and hypotenuse \(x\), the Pythagorean theorem is \(x=\sqrt{a^{2}+b^{2}}\). So \(x=\sqrt{(7.3)^{2}+(12.9)^{2}}\).
\[

$$\begin{align*} x&=\sqrt{53.29 + 166.41}\\ &=\sqrt{219.7}\\ &\approx14.82\text{ mi} \end{align*}$$

\]

Step2: Apply Pythagorean theorem for second triangle

For a right - triangle with hypotenuse \(x\), one side \(a = 12\) mi and the other side \(b = 35\) mi, by the Pythagorean theorem \(x=\sqrt{a^{2}+b^{2}}\). So \(x=\sqrt{(12)^{2}+(35)^{2}}\).
\[

$$\begin{align*} x&=\sqrt{144 + 1225}\\ &=\sqrt{1369}\\ & = 37\text{ mi} \end{align*}$$

\]

Answer:

14.82 mi
37 mi