One of the legs of a right triangle measures 8cm and its hypotenuse measures 17cm. Find the measure of the other leg. If necessary, round to the nearest tenth. Answer: cm

Identify Known Sides: Identify the known sides of the right triangle and the unknown side we need to find. We know one leg (a) is 8 cm, and the hypotenuse (c) is 17 cm. We need to find the other leg (b).Use Pythagorean Theorem: Use the Pythagorean Theorem to set up the equation to find the unknown leg. The Pythagorean Theorem states that in a right triangle, 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.Plug in Values: Plug in the known values into the Pythagorean Theorem and solve for b. We have a = 8 cm and c = 17 cm. Plugging these into the equation gives us: 8^2 + b^2 = 17^2.Calculate Squares: Calculate the squares of the known sides. 8^2 = 64 and 17^2 = 289. So, the equation becomes 64 + b^2 = 289.Subtract and Isolate: Subtract 64 from both sides of the equation to isolate b^2. b^2 = 289 - 64. b^2 = 225.Take Square Root: Take the square root of both sides to solve for b. b = sqrt(225). b = 15.

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One of the legs of a right triangle measures
8cm and its hypotenuse measures
17cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
cm

One of the legs of a right triangle measures $8 \mathrm{~cm}$ and its hypotenuse measures $17 \mathrm{~cm}$ . Find the measure of the other leg. 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

8 \mathrm{~cm}

and its hypotenuse measures

17 \mathrm{~cm}

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

\newline

Answer:

\square

\mathrm{cm}

Identify Known Sides: Identify the known sides of the right triangle and the unknown side we need to find. $\newline$ We know one leg $a$ is $8$ cm, and the hypotenuse $c$ is $17$ cm. We need to find the other leg $b$ .
Use Pythagorean Theorem: Use the Pythagorean Theorem to set up the equation to find the unknown leg. $\newline$ The Pythagorean Theorem states that in a right triangle, 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 $a^2 + b^2 = c^2$ .
Plug in Values: Plug in the known values into the Pythagorean Theorem and solve for $b$ . We have $a = 8$ cm and $c = 17$ cm. Plugging these into the equation gives us: $8^2 + b^2 = 17^2$ .
Calculate Squares: Calculate the squares of the known sides. $\newline$ $8^2 = 64$ and $17^2 = 289$ . $\newline$ So, the equation becomes $64 + b^2 = 289$ .
Subtract and Isolate: Subtract $64$ from both sides of the equation to isolate $b^2$ . $\newline$ $b^2 = 289 - 64.$ $\newline$ $b^2 = 225.$
Take Square Root: Take the square root of both sides to solve for $b$ . $b = \sqrt{225}$ . $b = 15$ .