If one of the legs of a triangle measures 10 cm and the hypotenuse measures 50.5 cm, find the length of the other leg? Round your answer to the nearest tenth if necessary.

1 answer

To find the length of the other leg of a right triangle when one leg and the hypotenuse are known, we can use the Pythagorean theorem, which states:

\[ a^2 + b^2 = c^2 \]

where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse.

In this case, let:

  • \( a = 10 \) cm (one leg)
  • \( c = 50.5 \) cm (hypotenuse)
  • \( b \) = length of the other leg

Using the Pythagorean theorem, we can rearrange the equation to find \( b \):

\[ b^2 = c^2 - a^2 \]

Now we'll substitute the given values:

\[ b^2 = (50.5)^2 - (10)^2 \]

Calculating each term:

\[ (50.5)^2 = 2550.25 \]

\[ (10)^2 = 100 \]

Now substitute these values back into the equation:

\[ b^2 = 2550.25 - 100 \]

\[ b^2 = 2450.25 \]

Now, take the square root of both sides to find \( b \):

\[ b = \sqrt{2450.25} \approx 49.5 \]

Thus, the length of the other leg is approximately \( 49.5 \) cm. Rounding to the nearest tenth, we find:

\[ \boxed{49.5} \text{ cm} \]