To find the length of the unknown leg of a right triangle when given one leg and the hypotenuse, you can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
Where:
- \(a\) and \(b\) are the legs of the triangle,
- \(c\) is the hypotenuse.
In your case, let's say:
- One leg, \(a\), is 14 m,
- The hypotenuse, \(c\), is 40.5 m.
We need to find the length of the other leg, \(b\).
- First, substitute the values into the Pythagorean theorem:
\[ 14^2 + b^2 = 40.5^2 \]
- Calculate \(14^2\) and \(40.5^2\):
\[ 196 + b^2 = 1640.25 \]
- Rearranging the equation to solve for \(b^2\):
\[ b^2 = 1640.25 - 196 \]
\[ b^2 = 1444.25 \]
- Now, take the square root to find \(b\):
\[ b = \sqrt{1444.25} \approx 38.0 \text{ m} \]
Rounding to one decimal place, the length of the unknown leg of the triangle is approximately:
38.0 m