Question

solve for c # 3 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 Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Here, if \(c\) is the hypotenuse, \(a = 5\) and \(b = 9\), the equation is \(5^{2}+9^{2}=c^{2}\), or if \(c\) is one of the non - hypotenuse sides (assuming 9 is the hypotenuse), the equation is \(c^{2}+5^{2}=9^{2}\). Since 9 is the longest given side, we use \(c^{2}+5^{2}=9^{2}\).

Step2: Simplify the equation

\(c^{2}+25 = 81\). Then, subtract 25 from both sides: \(c^{2}=81 - 25\), so \(c^{2}=56\).

Step3: Solve for \(c\)

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

Answer:

\(c\approx7.5\)