One of the legs of a right triangle measures 9cm and the other leg measures 10cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth. Answer: cm

Identify Triangle Legs: Identify the lengths of the legs of the right triangle. We know one leg measures 9cm and the other measures 10cm. These will be used to find the hypotenuse using the Pythagorean Theorem.Write Pythagorean Theorem: Write down the Pythagorean Theorem. 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). The formula is a^2 + b^2 = c^2.Plug Known Values: Plug the known values into the Pythagorean Theorem. Using the lengths of the legs, we have 9^2 + 10^2 = c^2.Calculate Leg Squares: Calculate the squares of the lengths of the legs. 9^2 = 81 and 10^2 = 100. So, we have 81 + 100 = c^2.Add Leg Squares: Add the squares of the lengths of the legs. 81 + 100 = 181. So, we have 181 = c^2.Find Square Root: Find the square root of the sum to solve for c. The square root of 181 is approximately 13.5. Therefore, c ≈ 13.5cm.

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One of the legs of a right triangle measures
9cm and the other leg measures
10cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
cm

One of the legs of a right triangle measures $9 \mathrm{~cm}$ and the other leg measures $10 \mathrm{~cm}$ . Find the measure of the hypotenuse. 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

9 \mathrm{~cm}

and the other leg measures

10 \mathrm{~cm}

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

\newline

Answer:

\square

\mathrm{cm}

Identify Triangle Legs: Identify the lengths of the legs of the right triangle. $\newline$ We know one leg measures $9\,\text{cm}$ and the other measures $10\,\text{cm}$ . These will be used to find the hypotenuse using the Pythagorean Theorem.
Write Pythagorean Theorem: Write down the Pythagorean Theorem. $\newline$ 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 $b$ . The formula is $a^2 + b^2 = c^2$ .
Plug Known Values: Plug the known values into the Pythagorean Theorem. $\newline$ Using the lengths of the legs, we have $9^2 + 10^2 = c^2$ .
Calculate Leg Squares: Calculate the squares of the lengths of the legs. $\newline$ $9^2 = 81$ and $10^2 = 100$ . So, we have $81 + 100 = c^2$ .
Add Leg Squares: Add the squares of the lengths of the legs. $\newline$ $81 + 100 = 181$ . So, we have $181 = c^2$ .
Find Square Root: Find the square root of the sum to solve for $c$ . The square root of $181$ is approximately $13.5$ . Therefore, $c \approx 13.5$ cm.