https://file.aiquickdraw.com/mathbot/file/1726840580696j1n5yucc.jpg

This diagram represents a right triangle, with the tree's height and the horizontal distance forming the two legs, and the hypotenuse (denoted as **c**) to be found.

We can use the **Pythagorean Theorem**, which is expressed as:
\[
a^2 + b^2 = c^2
\]
Here:
- \( a = 10 \, \text{feet} \) (horizontal distance),
- \( b = 30 \, \text{feet} \) (height of the tree),
- \( c \) is the hypotenuse we need to find.

Let's calculate:

\[
10^2 + 30^2 = c^2
\]
\[
100 + 900 = c^2
\]
\[
c^2 = 1000
\]
\[
c = \sqrt{1000} \approx 31.62 \, \text{feet}
\]

So, the length of **c** is approximately **31.62 feet**.

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:
1. How does the Pythagorean theorem apply to real-world scenarios like this one?
2. What would the hypotenuse be if the height of the tree were 40 feet instead of 30?
3. How does changing the horizontal distance affect the length of the hypotenuse?
4. Can you calculate the angles in this right triangle using trigonometric functions?
5. What is the significance of the hypotenuse in the context of triangle geometry?

**Tip:** Always make sure the triangle is a right triangle before applying the Pythagorean theorem!

Find the length of the hypotenuse (c) for a right triangle where one leg is 10 feet and the other leg is 30 feet.

Learn how to calculate the hypotenuse of a right triangle where one leg is 10 feet and the other leg is 30 feet. This problem applies the Pythagorean Theorem (a^2 + b^2 = c^2) and is suitable for students in Grades 6-8.

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