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 $c$. If the two legs of the right - triangle are $a = 5$ and $b = 9$, the Pythagorean theorem states that $a^{2}+b^{2}=c^{2}$. So the equation is $5^{2}+9^{2}=c^{2}$.

Step2: Calculate the left - hand side

$5^{2}=25$ and $9^{2}=81$, so $25 + 81=c^{2}$, which simplifies to $c^{2}=106$.

Step3: Solve for $c$

Taking the square root of both sides, $c=\sqrt{106}$.

Step4: Round to the nearest tenth

$\sqrt{106}\approx10.3$.

Answer:

$c\approx10.3$