Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point) the left side is 20 , the longer slant is 30.the shape is a right-angle Round to the nearest hundredth.
To find the unknown side length in a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the left side is given as 20 and the longer slant is given as 30. Let's call the unknown side length "x."
Applying the Pythagorean theorem, we can set up the following equation:
20^2 + x^2 = 30^2
Simplifying the equation:
400 + x^2 = 900
Now, subtracting 400 from both sides:
x^2 = 900 - 400
x^2 = 500
Finally, taking the square root of both sides:
x ≈ √500
Using a calculator or simplifying further:
x ≈ 22.36
Therefore, the unknown side length, rounded to the nearest hundredth, is approximately 22.36.