Question

problem 1: find the missing side using the pythagorean theorem ($a^2 + b^2 = c^2$), find the length of the missing side of the right triangle shown. the side lengths are given in units. show your work. be precise!

Explanation:

Step1: Identify known values

Given: right triangle, one leg $a=3$, hypotenuse $c=5$ (assuming the marked side is the hypotenuse, standard for this common triangle)

Step2: Rearrange Pythagorean theorem

To solve for missing leg $b$:
$b^2 = c^2 - a^2$

Step3: Substitute values

$b^2 = 5^2 - 3^2 = 25 - 9 = 16$

Step4: Solve for $b$

$b = \sqrt{16} = 4$

Answer:

4 units