The hypotenuse of a right triangle measures 13cm and one of its legs measures 5cm. Find the measure of the other leg. If necessary, round to the nearest tenth. Answer: cm

Identify sides and theorem: Identify the known sides of the right triangle and the Pythagorean theorem. We know one leg (a) measures 5 cm, and the hypotenuse (c) measures 13 cm. We need to find the other leg (b). The Pythagorean theorem states that a^2 + b^2 = c^2.Plug values into theorem: Plug the known values into the Pythagorean theorem to find the unknown leg (b). We have 5^2 + b^2 = 13^2.Calculate squares: Calculate the squares of the known values. 5^2 = 25 and 13^2 = 169. So, we have 25 + b^2 = 169.Subtract to solve: Subtract 25 from both sides of the equation to solve for b^2. b^2 = 169 - 25. b^2 = 144.Take square root: Take the square root of both sides to solve for b. b = sqrt(144). b = 12.Check result: Check the result to ensure it makes sense in the context of the problem. Since 5^2 + 12^2 equals 25 + 144, which is 169, and 169 is the square of 13, our calculations are correct.

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The hypotenuse of a right triangle measures
13cm and one of its legs measures
5cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
cm

The hypotenuse of a right triangle measures $13 \mathrm{~cm}$ and one of its legs measures $5 \mathrm{~cm}$ . Find the measure of the other leg. If necessary, round to the nearest tenth. $\newline$ Answer: $\square$ $\mathrm{cm}$

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Q. The hypotenuse of a right triangle measures

13 \mathrm{~cm}

and one of its legs measures

5 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

Answer:

\square

\mathrm{cm}

Identify sides and theorem: Identify the known sides of the right triangle and the Pythagorean theorem. $\newline$ We know one leg $a$ measures $5$ cm, and the hypotenuse $c$ measures $13$ cm. We need to find the other leg $b$ . $\newline$ The Pythagorean theorem states that $a^2 + b^2 = c^2$ .
Plug values into theorem: Plug the known values into the Pythagorean theorem to find the unknown leg $b$ . We have $5^2 + b^2 = 13^2$ .
Calculate squares: Calculate the squares of the known values. $\newline$ $5^2 = 25$ and $13^2 = 169$ . $\newline$ So, we have $25 + b^2 = 169$ .
Subtract to solve: Subtract $25$ from both sides of the equation to solve for $b^2$ . $\newline$ $b^2 = 169 - 25.$ $\newline$ $b^2 = 144.$
Take square root: Take the square root of both sides to solve for $b$ . $b = \sqrt{144}$ . $b = 12$ .
Check result: Check the result to ensure it makes sense in the context of the problem. $\newline$ Since $5^2 + 12^2$ equals $25 + 144$ , which is $169$ , and $169$ is the square of $13$ , our calculations are correct.