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One of the legs of a right triangle measures
7cm and its hypotenuse measures
9cm.
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 $7 \mathrm{~cm}$ and its hypotenuse measures $9 \mathrm{~cm}$ . $\newline$ Find the measure of the other leg. If necessary, round to the nearest tenth. $\newline$ Answer: $\square$ $\mathrm{cm}$

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Pythagorean theorem

Full solution

Q. One of the legs of a right triangle measures

7 \mathrm{~cm}

and its hypotenuse measures

9 \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 $7$ cm, and the hypotenuse $c$ is $9$ cm. We need to find the other leg $b$ . $\newline$ According to the Pythagorean Theorem, $a^2 + b^2 = c^2$ .
Apply Pythagorean Theorem: Plug the known values into the Pythagorean Theorem to find the unknown leg $b$ . $7^2 + b^2 = 9^2$ $49 + b^2 = 81$
Isolate $b^2$ : Subtract $49$ from both sides of the equation to isolate $b^2$ . $b^2 = 81 - 49$ $b^2 = 32$
Solve for $b$ : Take the square root of both sides to solve for $b$ . $b = \sqrt{32}$ $b \approx 5.7$ (rounded to the nearest tenth)

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