Question

If a right triangle has a leg that is 6 ft. long and the hypotenuse is 12 ft. long, how long is the other leg? Round to the nearest tenth.(1 point)

Answer 1

Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point)

Answer 2

To find the length of the other leg in a right triangle, we can use the Pythagorean theorem, which states:

\[ a^2 + b^2 = c^2 \]

where \( c \) is the length of the hypotenuse and \( a \) and \( b \) are the lengths of the legs.

In the given triangle:

- One leg (let's call it \( a \)) is 6 ft.
- The hypotenuse (let's call it \( c \)) is 12 ft.
- We need to find the length of the other leg (let's call it \( b \)).

Using the Pythagorean theorem:

\[
6^2 + b^2 = 12^2
\]

Calculating the squares:

\[
36 + b^2 = 144
\]

Now, subtract 36 from both sides:

\[
b^2 = 144 - 36
\]
\[
b^2 = 108
\]

Now take the square root of both sides to find \( b \):

\[
b = \sqrt{108}
\]

To simplify \( \sqrt{108} \):

\[
\sqrt{108} = \sqrt{36 \times 3} = 6\sqrt{3}
\]

Now, we can calculate \( 6\sqrt{3} \). The approximate value of \( \sqrt{3} \) is about 1.732.

So:

\[
b \approx 6 \times 1.732 \approx 10.392
\]

Rounding to the nearest tenth:

\[
b \approx 10.4 \text{ ft}
\]

Thus, the length of the other leg is approximately **10.4 ft**.

Answer 3

To help you find the unknown side length in a triangle, I need more specific details about the triangle in question, such as:

1. What type of triangle is it (right triangle, acute triangle, obtuse triangle)?
2. What information do you have (lengths of the sides, angles, etc.)?

Please provide the necessary details so I can assist you accurately!