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

Let the hypotenuse be 9 and the two legs be 5 and c. The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$. Here, if we assume the hypotenuse is 9 and one leg is 5 and the other leg is c, the equation is $c^{2}+5^{2}=9^{2}$.

Step2: Simplify the equation

$c^{2}+25 = 81$. Then, subtract 25 from both sides: $c^{2}=81 - 25=56$.

Step3: Solve for c

Take the square root of both sides: $c=\sqrt{56}$. Since c represents a side - length, we consider the positive square root. $c=\sqrt{4\times14}=2\sqrt{14}\approx 7.5$.

Answer:

$c\approx7.5$