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.





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Answer 1

To find the length of the other leg of the triangle, we can use the Pythagorean theorem, which states that in a right triangle:

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

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

Given:
- One leg \( a = 10 \) cm
- Hypotenuse \( c = 50.5 \) cm

We need to find the length of the other leg \( b \). Rearranging the Pythagorean theorem gives us:

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

Now, we will substitute the known values into the equation:

1. Calculate \( c^2 \):
\[
c^2 = (50.5)^2 = 2550.25
\]

2. Calculate \( a^2 \):
\[
a^2 = (10)^2 = 100
\]

3. Substitute values into the rearranged equation:
\[
b^2 = 2550.25 - 100 = 2450.25
\]

4. Now, take the square root to find \( b \):
\[
b = \sqrt{2450.25} \approx 49.5
\]

Thus, the length of the other leg, rounded to the nearest tenth, is:

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