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The given image shows a right triangle where the playground slide serves as the hypotenuse, measuring 10 feet, and the base of the slide is 8 feet from the base of the ladder. We are tasked with determining the height of the ladder, which forms the vertical side of the right triangle.

We can use the **Pythagorean theorem** to solve for the height of the ladder. The theorem states that for a right triangle:

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

Where:
- \( a \) is the height (the unknown we need to find),
- \( b = 8 \) feet (the base of the triangle),
- \( c = 10 \) feet (the hypotenuse, the length of the slide).

Let's solve for \( a \):

\[
a^2 + 8^2 = 10^2
\]
\[
a^2 + 64 = 100
\]
\[
a^2 = 100 - 64
\]
\[
a^2 = 36
\]
\[
a = \sqrt{36} = 6
\]

Therefore, the height of the ladder is **6 feet**.

The correct answer is **D. 6**.

Would you like further details on this, or do you have any questions? Here are some related questions:

1. How is the Pythagorean theorem used in real-world applications?
2. What are the properties of a right triangle?
3. Can the Pythagorean theorem be applied to all triangles?
4. How can we calculate the hypotenuse if the two legs of a triangle are known?
5. What are some other methods to calculate the height of an object using trigonometry?

**Tip**: Always remember that the Pythagorean theorem only applies to right-angled triangles.

A playground slide is 10 feet long, and the base of the slide is 8 feet from the base of a ladder, as shown in the figure. If the ladder is perpendicular to the ground, what is the height, in feet, of the ladder?

Learn how to calculate the height of a ladder using the Pythagorean theorem. This problem involves a right triangle with a 10-foot slide and an 8-foot base. Suitable for students in Grades 7-9.

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