find the unknown side length in the given triangle if the hypotenuse is 30 and one leg is 20. rounded to the nearest hundredth
To find the unknown side length, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's assume the unknown leg is represented by the variable $x$.
Using the Pythagorean theorem, we have:
$x^2 + 20^2 = 30^2$
Simplifying, we get:
$x^2 + 400 = 900$
Subtracting 400 from both sides:
$x^2 = 500$
Taking the square root of both sides:
$x = \sqrt{500}$
Evaluating this on a calculator, we find:
$x \approx 22.36$
Hence, the unknown side length, rounded to the nearest hundredth, is approximately 22.36.