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.
1 answer