One of the legs of a right triangle measures 6cm and the other leg measures 8cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth. Answer: cm

Identify legs and relationship: Identify the legs of the right triangle and the relationship between the legs and the hypotenuse. The legs are 6 cm and 8 cm. According to the Pythagorean theorem, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). a^2 + b^2 = c^2Plug values into theorem: Plug the values of the legs into the Pythagorean theorem to find the hypotenuse. 6^2 + 8^2 = c^2 36 + 64 = c^2Add squares for hypotenuse: Add the squares of the legs to find the square of the hypotenuse. 36 + 64 = 100 c^2 = 100Take square root to solve: Take the square root of both sides of the equation to solve for c, the hypotenuse. sqrt(c^2) = sqrt(100) c = 10Conclude hypotenuse measure: Since the problem asks for the measure of the hypotenuse and no rounding is necessary, we can conclude that the hypotenuse measures 10 cm. Answer: 10 cm

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One of the legs of a right triangle measures
6cm and the other leg measures
8cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
cm

One of the legs of a right triangle measures $6 \mathrm{~cm}$ and the other leg measures $8 \mathrm{~cm}$ . 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

6 \mathrm{~cm}

and the other leg measures

8 \mathrm{~cm}

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

\newline

Answer:

\square

\mathrm{cm}

Identify legs and relationship: Identify the legs of the right triangle and the relationship between the legs and the hypotenuse. $\newline$ The legs are $6\,\text{cm}$ and $8\,\text{cm}$ . According to the Pythagorean theorem, the square of the hypotenuse ( $c$ ) is equal to the sum of the squares of the other two sides ( $a$ and $b$ ). $\newline$ $a^2 + b^2 = c^2$
Plug values into theorem: Plug the values of the legs into the Pythagorean theorem to find the hypotenuse. $\newline$ $6^2 + 8^2 = c^2$ $\newline$ $36 + 64 = c^2$
Add squares for hypotenuse: Add the squares of the legs to find the square of the hypotenuse. $\newline$ $36 + 64 = 100$ $\newline$ $c^2 = 100$
Take square root to solve: Take the square root of both sides of the equation to solve for $c$ , the hypotenuse. $\sqrt{c^2} = \sqrt{100}$ $c = 10$
Conclude hypotenuse measure: Since the problem asks for the measure of the hypotenuse and no rounding is necessary, we can conclude that the hypotenuse measures $10\,\text{cm}$ . $\newline$ Answer: $10\,\text{cm}$