One of the legs of a right triangle measures 5cm and the other leg measures 12cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth. Answer: cm

Identify Legs and Formula: Identify the legs of the right triangle and the formula to use. We have a right triangle with legs of 5 cm and 12 cm. We will use the Pythagorean Theorem to find the length of the hypotenuse, which 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).Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the length of the hypotenuse. Using the formula a^2 + b^2 = c^2, where a and b are the lengths of the legs, and c is the length of the hypotenuse, we plug in the values: 5^2 + 12^2 = c^2Calculate Squares of Legs: Calculate the squares of the lengths of the legs. 5^2 = 25 12^2 = 144 Now add these two values to find c^2: 25 + 144 = c^2Solve for c^2: Solve for c^2. 25 + 144 = 169 c^2 = 169Find Hypotenuse Length: Find the length of the hypotenuse by taking the square root of c^2. sqrt(c^2) = sqrt(169) c = 13Round Answer: Round the answer to the nearest tenth if necessary. Since the value of c is an exact integer, there is no need to round. The length of the hypotenuse is 13 cm.

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One of the legs of a right triangle measures
5cm and the other leg measures
12cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
cm

One of the legs of a right triangle measures $5 \mathrm{~cm}$ and the other leg measures $12 \mathrm{~cm}$ . $\newline$ Find the measure of the hypotenuse. If necessary, round to the nearest tenth. $\newline$ Answer: $\square$ $\mathrm{cm}$

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Algebra 2

Pythagorean Theorem and its converse

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Q. One of the legs of a right triangle measures

5 \mathrm{~cm}

and the other leg measures

12 \mathrm{~cm}

\newline

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

\newline

Answer:

\square

\mathrm{cm}

Identify Legs and Formula: Identify the legs of the right triangle and the formula to use. $\newline$ We have a right triangle with legs of $5\,\text{cm}$ and $12\,\text{cm}$ . We will use the Pythagorean Theorem to find the length of the hypotenuse, which 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 $b$ ).
Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the length of the hypotenuse. $\newline$ Using the formula $a^2 + b^2 = c^2$ , where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse, we plug in the values: $\newline$ $5^2 + 12^2 = c^2$
Calculate Squares of Legs: Calculate the squares of the lengths of the legs. $\newline$ $5^2 = 25$ $\newline$ $12^2 = 144$ $\newline$ Now add these two values to find $c^2$ : $\newline$ $25 + 144 = c^2$
Solve for $c^2$ : Solve for $c^2$ . $\newline$ $25 + 144 = 169$ $\newline$ $c^2 = 169$
Find Hypotenuse Length: Find the length of the hypotenuse by taking the square root of $c^2$ . $\newline$ $\sqrt{c^2} = \sqrt{169}$ $\newline$ $c = 13$
Round Answer: Round the answer to the nearest tenth if necessary. $\newline$ Since the value of $c$ is an exact integer, there is no need to round. The length of the hypotenuse is $13\,\text{cm}$ .