One of the legs of a right triangle measures 7cm and the other leg measures 3cm. 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. The legs of the triangle are 7 cm and 3 cm. We will use the Pythagorean Theorem to find 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). Formula: a^2 + b^2 = c^2Plug values into theorem: Plug the values of the legs into the Pythagorean Theorem. We have a = 7 cm and b = 3 cm. So, we get: 7^2 + 3^2 = c^2Calculate squares of legs: Calculate the squares of the lengths of the legs. 7^2 = 49 3^2 = 9 Now add these two values to get the square of the hypotenuse. 49 + 9 = c^2Add results for hypotenuse: Add the results to find the square of the hypotenuse. 49 + 9 = 58 So, c^2 = 58Take square root for c: Take the square root of both sides to solve for c. sqrt(c^2) = sqrt(58) c = sqrt(58)Round to nearest tenth: Round the result to the nearest tenth, if necessary. sqrt(58) is approximately 7.6 when rounded to the nearest tenth.

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One of the legs of a right triangle measures
7cm and the other leg measures
3cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
cm

One of the legs of a right triangle measures $7 \mathrm{~cm}$ and the other leg measures $3 \mathrm{~cm}$ . Find the measure of the hypotenuse. If necessary, round to the nearest tenth. $\newline$ Answer: $\square$ $\mathrm{cm}$

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Math Problems

Algebra 2

Pythagorean Theorem and its converse

Full solution

Q. One of the legs of a right triangle measures

7 \mathrm{~cm}

and the other leg measures

3 \mathrm{~cm}

. 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. $\newline$ The legs of the triangle are $7\,\text{cm}$ and $3\,\text{cm}$ . We will use the Pythagorean Theorem to find 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 $b$ ). $\newline$ Formula: $a^2 + b^2 = c^2$
Plug values into theorem: Plug the values of the legs into the Pythagorean Theorem. $\newline$ We have $a = 7\,\text{cm}$ and $b = 3\,\text{cm}$ . So, we get: $\newline$ $7^2 + 3^2 = c^2$
Calculate squares of legs: Calculate the squares of the lengths of the legs. $\newline$ $7^2 = 49$ $\newline$ $3^2 = 9$ $\newline$ Now add these two values to get the square of the hypotenuse. $\newline$ $49 + 9 = c^2$
Add results for hypotenuse: Add the results to find the square of the hypotenuse. $\newline$ $49 + 9 = 58$ $\newline$ So, $c^2 = 58$
Take square root for $c$ : Take the square root of both sides to solve for $c$ . $\sqrt{c^2} = \sqrt{58}$ $c = \sqrt{58}$
Round to nearest tenth: Round the result to the nearest tenth, if necessary. $\sqrt{58}$ is approximately $7.6$ when rounded to the nearest tenth.