One of the legs of a right triangle measures 12cm and its hypotenuse measures 13cm. Find the measure of the other leg. If necessary, round to the nearest tenth. Answer: cm

Identify Known and Unknown: Identify the known sides of the right triangle and the unknown side we need to find. We know one leg (a) is 12 cm, and the hypotenuse (c) is 13 cm. We need to find the length of the other leg (b).Use Pythagorean Theorem: Use the Pythagorean Theorem to set up the equation for the right triangle. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). So, we have: a^2 + b^2 = c^2.Plug in Known Values: Plug in the known values into the Pythagorean Theorem. We have: 12^2 + b^2 = 13^2.Calculate Squares: Calculate the squares of the known sides. 12^2 = 144 and 13^2 = 169. So, we have: 144 + b^2 = 169.Subtract to Solve: Subtract 144 from both sides of the equation to solve for b^2. b^2 = 169 - 144.Calculate Difference: Calculate the difference to find b^2. b^2 = 25.Take Square Root: Take the square root of both sides to solve for b. b = sqrt(25).Calculate Final Length: Calculate the square root of 25 to find the length of the other leg. b = 5.

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One of the legs of a right triangle measures
12cm and its hypotenuse measures
13cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
cm

One of the legs of a right triangle measures $12 \mathrm{~cm}$ and its hypotenuse measures $13 \mathrm{~cm}$ . Find the measure of the other leg. If necessary, round to the nearest tenth. $\newline$ Answer: $\square$ $\mathrm{cm}$

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Q. One of the legs of a right triangle measures

12 \mathrm{~cm}

and its hypotenuse measures

13 \mathrm{~cm}

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

\newline

Answer:

\square

\mathrm{cm}

Identify Known and Unknown: Identify the known sides of the right triangle and the unknown side we need to find. We know one leg $a$ is $12$ cm, and the hypotenuse $c$ is $13$ cm. We need to find the length of the other leg $b$ .
Use Pythagorean Theorem: Use the Pythagorean Theorem to set up the equation for the right triangle. $\newline$ The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse $c$ is equal to the sum of the squares of the lengths of the other two sides $a$ and $b$ . $\newline$ So, we have: $a^2 + b^2 = c^2$ .
Plug in Known Values: Plug in the known values into the Pythagorean Theorem. $\newline$ We have: $12^2 + b^2 = 13^2$ .
Calculate Squares: Calculate the squares of the known sides. $\newline$ $12^2 = 144$ and $13^2 = 169$ . $\newline$ So, we have: $144 + b^2 = 169$ .
Subtract to Solve: Subtract $144$ from both sides of the equation to solve for $b^2$ . $\newline$ $b^2 = 169 - 144.$
Calculate Difference: Calculate the difference to find $b^2$ . $\newline$ $b^2 = 25$ .
Take Square Root: Take the square root of both sides to solve for $b$ . $b = \sqrt{25}$ .
Calculate Final Length: Calculate the square root of $25$ to find the length of the other leg. $b = 5$ .