One of the legs of a right triangle measures 6cm and its hypotenuse measures 10cm. Find the measure of the other leg. If necessary, round to the nearest tenth. Answer: cm

Identify sides and unknown: Identify the known sides of the right triangle and the unknown side we need to find. We know one leg (a) is 6 cm, and the hypotenuse (c) is 10 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, c^2 = a^2 + b^2.Plug in known values: Plug in the known values into the Pythagorean Theorem equation. We have a = 6 cm and c = 10 cm, so: 10^2 = 6^2 + b^2.Calculate squares: Calculate the square of the known sides. 10^2 = 100 and 6^2 = 36. So, 100 = 36 + b^2.Isolate variable b: Isolate the variable b^2 to solve for b. Subtract 36 from both sides of the equation to get b^2 on its own. 100 - 36 = b^2.Calculate b^2: Calculate the value of b^2. 100 - 36 = 64. So, b^2 = 64.Take square root: Take the square root of both sides to solve for b. sqrt(b^2) = sqrt(64). b = 8.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

One of the legs of a right triangle measures
6cm and its hypotenuse measures
10cm. 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 $6 \mathrm{~cm}$ and its hypotenuse measures $10 \mathrm{~cm}$ . Find the measure of the other leg. If necessary, round to the nearest tenth. $\newline$ Answer: $\square$ $\mathrm{cm}$

View step-by-step help

Full solution

Q. One of the legs of a right triangle measures

6 \mathrm{~cm}

and its hypotenuse measures

10 \mathrm{~cm}

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

\newline

Answer:

\square

\mathrm{cm}

Identify sides and unknown: Identify the known sides of the right triangle and the unknown side we need to find. We know one leg $a$ is $6$ cm, and the hypotenuse $c$ is $10$ 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, $c^2 = a^2 + b^2$ .
Plug in known values: Plug in the known values into the Pythagorean Theorem equation. $\newline$ We have $a = 6\, \text{cm}$ and $c = 10\, \text{cm}$ , so: $\newline$ $10^2 = 6^2 + b^2$ .
Calculate squares: Calculate the square of the known sides. $\newline$ $10^2 = 100$ and $6^2 = 36$ . $\newline$ So, $100 = 36 + b^2$ .
Isolate variable b: Isolate the variable $b^2$ to solve for $b$ . $\newline$ Subtract $36$ from both sides of the equation to get $b^2$ on its own. $\newline$ $100 - 36 = b^2$ .
Calculate $b^2$ : Calculate the value of $b^2$ . $100 - 36 = 64$ . So, $b^2 = 64$ .
Take square root: Take the square root of both sides to solve for $b$ . $\sqrt{b^2} = \sqrt{64}$ . $b = 8$ .