Question

One of the legs of a right triangle measures 5 cm and its hypotenuse measures 10 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answer 1

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

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

where \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse. In this case, we know one leg \(a = 5\) cm and the hypotenuse \(c = 10\) cm. We need to find the length of the other leg \(b\).

Substituting the known values into the Pythagorean theorem gives us:

\[
5^2 + b^2 = 10^2
\]

Calculating the squares:

\[
25 + b^2 = 100
\]

Next, subtract 25 from both sides:

\[
b^2 = 100 - 25
\]
\[
b^2 = 75
\]

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

\[
b = \sqrt{75}
\]

We can simplify \(\sqrt{75}\):

\[
b = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}
\]

Now, we can approximate \(b\) using the value of \(\sqrt{3} \approx 1.732\):

\[
b \approx 5 \times 1.732 \approx 8.66
\]

Rounding to the nearest tenth, we find:

\[
b \approx 8.7 \text{ cm}
\]

Thus, the measure of the other leg is approximately **8.7 cm**.