https://file.aiquickdraw.com/mathbot/file/1726705019691i30jer41.jpg

Given the information in the image:

1. The hypotenuse of a right triangle is \( 10 \) feet.
2. The shorter leg of the triangle is \( 2 \) feet.

We need to find the lengths of the sides of the triangle.

### Step-by-step Solution:
Since we are dealing with a right triangle, we can use the Pythagorean theorem:

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

Where:
- \( a \) is the shorter leg (\( 2 \) feet),
- \( b \) is the longer leg (unknown),
- \( c \) is the hypotenuse (\( 10 \) feet).

Plugging in the values:

\[
2^2 + b^2 = 10^2
\]

\[
4 + b^2 = 100
\]

Subtract \( 4 \) from both sides:

\[
b^2 = 96
\]

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

\[
b = \sqrt{96} \approx 9.8 \, \text{feet}
\]

### Final Answer:
- Length of the shorter leg: \( 2 \) feet
- Length of the longer leg: \( \sqrt{96} \approx 9.8 \) feet
- Length of the hypotenuse: \( 10 \) feet

Would you like a detailed explanation of any part of this solution, or do you have any other questions?

### Additional Related Questions:
1. How do you use the Pythagorean theorem to find the hypotenuse if both legs are known?
2. What are the properties of a right triangle?
3. How would you solve the problem if only the legs were known and the hypotenuse was unknown?
4. How do you simplify square roots like \( \sqrt{96} \) into a more exact form?
5. What are some real-world applications of the Pythagorean theorem?

### Tip:
When dealing with right triangles, the Pythagorean theorem is a powerful tool to find missing side lengths when any two sides are known.

The hypotenuse of a right triangle is 10 feet long. The shorter leg is 2 feet shorter than the longer leg. Find the side lengths of the triangle.

This page shows how to solve a right triangle problem where the hypotenuse is 10 feet and the shorter leg is 2 feet. Learn step-by-step how to use the Pythagorean theorem to calculate the unknown side of the triangle.

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