Question

find the length of the third side. if necessary, round to the nearest tenth. 14 24

Explanation:

Step1: Identify Pythagorean theorem

We use the Pythagorean theorem for right triangles: $a^2 + b^2 = c^2$, where $c$ is the hypotenuse, $b=14$, $c=24$, and $a$ is the unknown side. Rearrange to solve for $a$: $a = \sqrt{c^2 - b^2}$

Step2: Substitute given values

Substitute $c=24$ and $b=14$ into the formula:
$a = \sqrt{24^2 - 14^2}$

Step3: Calculate squared terms

Compute the squares:
$24^2 = 576$, $14^2 = 196$
$a = \sqrt{576 - 196}$

Step4: Simplify the expression

Subtract and take the square root:
$a = \sqrt{380} \approx 19.5$

Answer:

19.5