One of the legs of a right triangle measures 8cm and the other leg measures 16cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth. Answer: cm

Identify Triangle Legs: Identify the legs of the right triangle and the relationship between the legs and the hypotenuse. The legs of the right triangle are given as 8 cm and 16 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). So, the equation is a^2 + b^2 = c^2.Substitute Values: Substitute the given values into the Pythagorean theorem. We have a = 8 cm and b = 16 cm. Plugging these values into the equation gives us: 8^2 + 16^2 = c^2.Calculate Squares: Calculate the squares of the given leg measurements. 8^2 = 64 and 16^2 = 256. Now, add these two values to find c^2. 64 + 256 = c^2.Add Results: Add the results to find the value of c^2. 64 + 256 = 320. So, c^2 = 320.Find Hypotenuse Length: Take the square root of c^2 to find the length of the hypotenuse. The square root of 320 is approximately 17.9 when rounded to the nearest tenth. So, c ≈ 17.9 cm.

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One of the legs of a right triangle measures
8cm and the other leg measures
16cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:

cm

One of the legs of a right triangle measures $8 \mathrm{~cm}$ and the other leg measures $16 \mathrm{~cm}$ . $\newline$ Find the measure of the hypotenuse. If necessary, round to the nearest tenth. $\newline$ Answer: $\square$ $\mathrm{cm}$

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Math Problems

Algebra 2

Pythagorean Theorem and its converse

Full solution

Q. One of the legs of a right triangle measures

8 \mathrm{~cm}

and the other leg measures

16 \mathrm{~cm}

\newline

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

\newline

Answer:

\square

\mathrm{cm}

Identify Triangle Legs: Identify the legs of the right triangle and the relationship between the legs and the hypotenuse. $\newline$ The legs of the right triangle are given as $8\,\text{cm}$ and $16\,\text{cm}$ . 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 $b$ ). $\newline$ So, the equation is $a^2 + b^2 = c^2$ .
Substitute Values: Substitute the given values into the Pythagorean theorem. $\newline$ We have $a = 8\,\text{cm}$ and $b = 16\,\text{cm}$ . Plugging these values into the equation gives us: $\newline$ $8^2 + 16^2 = c^2$ .
Calculate Squares: Calculate the squares of the given leg measurements. $\newline$ $8^2 = 64$ and $16^2 = 256$ . Now, add these two values to find $c^2$ . $\newline$ $64 + 256 = c^2$ .
Add Results: Add the results to find the value of $c^2$ . $64 + 256 = 320$ . So, $c^2 = 320$ .
Find Hypotenize Length: Take the square root of $c^2$ to find the length of the hypotenuse. $\newline$ The square root of $320$ is approximately $17.9$ when rounded to the nearest tenth. $\newline$ So, $c \approx 17.9$ cm.