The hypotenuse of a right triangle measures 15cm and one of its legs measures 12 cm. Find the measure of the other leg. If necessary, round to the nearest tenth. Answer: cm

Identify sides and formula: Identify the known sides of the right triangle and the Pythagorean theorem formula. We know the hypotenuse (c) is 15 cm and one leg (a) is 12 cm. 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). Formula: a^2 + b^2 = c^2Plug known values: Plug the known values into the Pythagorean theorem to find the length of the other leg (b). We have a = 12 cm and c = 15 cm. So, we need to solve for b. 12^2 + b^2 = 15^2Calculate squares: Calculate the square of the known leg and the hypotenuse. 12^2 = 144 15^2 = 225Subtract squares: Subtract the square of the known leg (a) from the square of the hypotenuse (c) to find the square of the other leg (b). 225 - 144 = b^2 b^2 = 81Find length of leg: Find the length of the other leg (b) by taking the square root of b^2. sqrt(b^2) = sqrt(81) b = 9

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The hypotenuse of a right triangle measures
15cm and one of its legs measures 12
cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
cm

The hypotenuse of a right triangle measures $15 \mathrm{~cm}$ and one of its legs measures $12$ $\mathrm{cm}$ . Find the measure of the other leg. If necessary, round to the nearest tenth. $\newline$ Answer: $\square$ $\mathrm{cm}$

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Q. The hypotenuse of a right triangle measures

15 \mathrm{~cm}

and one of its legs measures

12

\mathrm{cm}

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

\newline

Answer:

\square

\mathrm{cm}

Identify sides and formula: Identify the known sides of the right triangle and the Pythagorean theorem formula. $\newline$ We know the hypotenuse $c$ is $15$ cm and one leg $a$ is $12$ cm. 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 $b$ . $\newline$ Formula: $a^2 + b^2 = c^2$
Plug known values: Plug the known values into the Pythagorean theorem to find the length of the other leg $b$ . We have $a = 12$ cm and $c = 15$ cm. So, we need to solve for $b$ . $12^2 + b^2 = 15^2$
Calculate squares: Calculate the square of the known leg and the hypotenuse. $\newline$ $12^2 = 144$ $\newline$ $15^2 = 225$
Subtract squares: Subtract the square of the known leg $a$ from the square of the hypotenuse $c$ to find the square of the other leg $b$ . $225 - 144 = b^2$ $b^2 = 81$
Find length of leg: Find the length of the other leg $b$ by taking the square root of $b^2$ . $\sqrt{b^2} = \sqrt{81}$ $b = 9$