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 right triangle, we can use the Pythagorean theorem, which states:

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

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

Let's denote:
- \( a = 10 \) cm (one leg)
- \( c = 50.5 \) cm (the hypotenuse)
- \( b \) = length of the other leg (which we want to find)

We can substitute the values we know into the Pythagorean theorem:

\[
10^2 + b^2 = 50.5^2
\]

Calculating \( 10^2 \) and \( 50.5^2 \):

\[
100 + b^2 = 2550.25
\]

Now, we can isolate \( b^2 \):

\[
b^2 = 2550.25 - 100
\]
\[
b^2 = 2450.25
\]

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

\[
b = \sqrt{2450.25}
\]

Now we calculate \( \sqrt{2450.25} \):

\[
b \approx 49.5
\]

Rounding to the nearest tenth, the length of the other leg \( b \) is:

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