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 first triangle

For a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\). Here \(c = 50\) km and \(a = 48\) km, we want to find \(b=x\). So \(x=\sqrt{50^{2}-48^{2}}\).
\[

$$\begin{align*} x&=\sqrt{(50 + 48)(50 - 48)}\\ &=\sqrt{98\times2}\\ &=\sqrt{196}\\ & = 14\text{ km} \end{align*}$$

\]

Step2: Apply Pythagorean theorem for second triangle

Here \(c = 15.8\) yd and \(a = 13.1\) yd, and we want to find \(b=x\). So \(x=\sqrt{15.8^{2}-13.1^{2}}\).
\[

$$\begin{align*} x&=\sqrt{(15.8 + 13.1)(15.8 - 13.1)}\\ &=\sqrt{28.9\times2.7}\\ &=\sqrt{78.03}\\ &\approx8.83\text{ yd} \end{align*}$$

\]

Answer:

14 km
8.83 yd