One of the legs of a right triangle measures 10 cm and the other leg measures 7 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Using the Pythagorean theorem, we have $c^2 = a^2 + b^2 = 10^2 + 7^2 = 100 + 49 = 149.$ Taking the square root of both sides, we find $c = \sqrt{149} \approx \boxed{12.2}$ cm.
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Using the Pythagorean theorem $a^2 + b^2 = c^2$, where $a$ and $b$ are the legs of the right triangle and $c$ is the hypotenuse, we can plug in the lengths of the legs:
$10^2 + 7^2 = c^2$
$100 + 49 = c^2$
$149 = c^2$
Taking the square root of both sides, we get:
$c = \sqrt{149} \approx 12.2$
Therefore, the length of the hypotenuse is approximately $\boxed{12.2}$ cm.
To find the measure of the hypotenuse of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs.
In this case, we have one leg measuring 10 cm and the other leg measuring 7 cm. Let's assign variables to these lengths. Let's call the hypotenuse "c", the leg measuring 10 cm as "a", and the leg measuring 7 cm as "b".
According to the Pythagorean theorem, we have the equation:
c^2 = a^2 + b^2
Substituting the values:
c^2 = 10^2 + 7^2
c^2 = 100 + 49
c^2 = 149
To find the measure of the hypotenuse (c), we need to take the square root of both sides of the equation:
c = √149
Using a calculator, we find that the square root of 149 is approximately 12.2.
Therefore, the measure of the hypotenuse is approximately 12.2 cm (rounded to the nearest tenth).