To find the missing side of a right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the hypotenuse (the longest side), and \(a\) and \(b\) are the other two sides.
You provided the lengths of two sides: 38 units and 9 units. We need to determine which side represents the hypotenuse. Let's assume the longest side (38 units) is the hypotenuse.
If that's the case, we can denote the sides as follows:
- \(c = 38\) (hypotenuse)
- \(a = 9\)
- \(b = ?\) (the missing side)
Now, we can plug these values into the Pythagorean theorem:
\[ 9^2 + b^2 = 38^2 \]
Calculating \(9^2\) and \(38^2\):
\[ 81 + b^2 = 1444 \]
Next, subtract \(81\) from both sides:
\[ b^2 = 1444 - 81 \] \[ b^2 = 1363 \]
Now, take the square root to find \(b\):
\[ b = \sqrt{1363} \approx 36.9 \]
Rounding to the nearest tenth, the missing side of the triangle is approximately 36.9 units.