Question

find the missing side length (include units). round to the nearest hundredth, if necessary.
find the missing side length (include units). round to the nearest hundredth, if necessary.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). In the first triangle, if \(a = 20\) mi, \(c=29\) mi, and we want to find \(b=x\). Then \(x=\sqrt{c^{2}-a^{2}}\).
\[x=\sqrt{29^{2}-20^{2}}=\sqrt{(29 + 20)(29 - 20)}=\sqrt{49\times9}=\sqrt{441}=21\text{ mi}\]

Step2: Apply Pythagorean theorem to the second triangle

In the second triangle, if \(a=x\), \(b = 30\) m, \(c = 34\) m. Then \(x=\sqrt{c^{2}-b^{2}}\).
\[x=\sqrt{34^{2}-30^{2}}=\sqrt{(34 + 30)(34 - 30)}=\sqrt{64\times4}=\sqrt{256}=16\text{ m}\]

Answer:

The first side length is \(21\) mi and the second side length is \(16\) m.