To find the unknown side length of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The formula is:
\[ c^2 = a^2 + b^2 \]
In this case:
- \( c \) is the length of the hypotenuse (the slanted line), which is 30.
- \( a \) is one of the other sides of the triangle, which is 20.
- \( b \) is the unknown side.
Rearranging the formula to solve for \( b \):
\[ b^2 = c^2 - a^2 \]
Now, substituting in the known values:
\[ b^2 = 30^2 - 20^2 \] \[ b^2 = 900 - 400 \] \[ b^2 = 500 \]
Next, take the square root of both sides to find \( b \):
\[ b = \sqrt{500} \] \[ b \approx 22.36 \]
Rounding to the nearest hundredth, the length of the unknown side is approximately \( 22.36 \).