Question

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.

Answer 1

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:

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