Question

set up an equation that can be used to solve for the missing side length. use c as your unknown. then, solve the equation and if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\), the formula is \(a^{2}+b^{2}=c^{2}\). Here, if we assume the two legs of the right - triangle are \(a = 5\) and \(b=c\) (unknown) and the hypotenuse \(c = 9\), then the equation is \(5^{2}+c^{2}=9^{2}\).

Step2: Simplify the equation

\[

$$\begin{align*} 25 + c^{2}&=81\\ c^{2}&=81 - 25\\ c^{2}&=56 \end{align*}$$

\]

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{56}\approx7.5\)

Answer:

Equation: \(5^{2}+c^{2}=9^{2}\)
\(c\approx7.5\)