One of the legs of a right triangle measures 3cm and its hypotenuse measures 5cm. 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 relationship between them. We know one leg (a) is 3 cm and the hypotenuse (c) is 5 cm. We need to find the other leg (b).Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the length of the other leg. The Pythagorean Theorem 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). So, a^2 + b^2 = c^2.Plug in Values: Plug in the known values and solve for the unknown leg (b). We have a = 3 cm and c = 5 cm. Therefore: 3^2 + b^2 = 5^2.Calculate Squares: Calculate the squares of the known sides. 3^2 = 9 and 5^2 = 25. So, 9 + b^2 = 25.Isolate for b: Isolate b^2 to solve for b. b^2 = 25 - 9. b^2 = 16.Find Value of b: Take the square root of both sides to find the value of b. √(b^2) = √16. b = 4.Check Answer: Check if the answer is reasonable. Since 3^2 + 4^2 = 9 + 16 = 25, which is equal to 5^2, our answer is correct.

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One of the legs of a right triangle measures
3cm and its hypotenuse measures
5cm.
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 $3 \mathrm{~cm}$ and its hypotenuse measures $5 \mathrm{~cm}$ . $\newline$ 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

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Q. One of the legs of a right triangle measures

3 \mathrm{~cm}

and its hypotenuse measures

5 \mathrm{~cm}

\newline

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 relationship between them. $\newline$ We know one leg $a$ is $3$ cm and the hypotenuse $c$ is $5$ cm. We need to find the other leg $b$ .
Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the length of the other leg. $\newline$ The Pythagorean Theorem 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 $b$ . $\newline$ So, $a^2 + b^2 = c^2$ .
Plug in Values: Plug in the known values and solve for the unknown leg $b$ . We have $a = 3$ cm and $c = 5$ cm. Therefore: $3^2 + b^2 = 5^2$ .
Calculate Squares: Calculate the squares of the known sides. $\newline$ $3^2 = 9$ and $5^2 = 25$ . $\newline$ So, $9 + b^2 = 25$ .
Isolate for $b$ : Isolate $b^2$ to solve for $b$ . $b^2 = 25 - 9$ . $b^2 = 16$ .
Find Value of b: Take the square root of both sides to find the value of b. $\sqrt{b^2} = \sqrt{16}$ . $b = 4$ .
Check Answer: Check if the answer is reasonable. $\newline$ Since $3^2 + 4^2 = 9 + 16 = 25$ , which is equal to $5^2$ , our answer is correct.