One of the legs of a right triangle measures 1cm 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 of the triangle are given as 1 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). Mathematically, this is represented as a^2 + b^2 = c^2.Substitute Values: Substitute the given values into the Pythagorean theorem. We have a = 1 cm and b = 8 cm. Plugging these values into the equation, we get: 1^2 + 8^2 = c^2.Calculate Squares: Calculate the squares of the given sides. 1^2 = 1 and 8^2 = 64. So, the equation becomes: 1 + 64 = c^2.Add Results: Add the results to find the square of the hypotenuse. 1 + 64 = 65, so c^2 = 65.Take Square Root: Take the square root of both sides to solve for c. sqrt(c^2) = sqrt(65), which gives us c = sqrt(65).Calculate and Round: Calculate the square root of 65 and, if necessary, round to the nearest tenth. sqrt(65) is approximately 8.1 when rounded to the nearest tenth.

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One of the legs of a right triangle measures
1cm 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 $1 \mathrm{~cm}$ 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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Algebra 2

Pythagorean Theorem and its converse

Full solution

Q. One of the legs of a right triangle measures

1 \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 of the triangle are given as $1\,\text{cm}$ 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 $b$ ). $\newline$ Mathematically, this is represented as $a^2 + b^2 = c^2$ .
Substitute Values: Substitute the given values into the Pythagorean theorem. $\newline$ We have $a = 1\,\text{cm}$ and $b = 8\,\text{cm}$ . Plugging these values into the equation, we get: $\newline$ $1^2 + 8^2 = c^2.$
Calculate Squares: Calculate the squares of the given sides. $\newline$ $1^2 = 1$ and $8^2 = 64$ . So, the equation becomes: $\newline$ $1 + 64 = c^2$ .
Add Results: Add the results to find the square of the hypotenuse. $\newline$ $1 + 64 = 65$ , so $c^2 = 65$ .
Take Square Root: Take the square root of both sides to solve for $c$ . $\sqrt{c^2} = \sqrt{65}$ , which gives us $c = \sqrt{65}$ .
Calculate and Round: Calculate the square root of $65$ and, if necessary, round to the nearest tenth. $\sqrt{65}$ is approximately $8.1$ when rounded to the nearest tenth.