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This problem involves trigonometry, specifically right triangle relationships. The ladder, wall, and ground form a right triangle, with the height of the ladder against the wall, the distance from the base of the ladder to the wall, and the length of the ladder as sides of the triangle. The height of the ladder is 15 feet, and the angle of inclination is 60°.

We can use the tangent function to solve for the distance from the base of the ladder to the wall. The tangent of an angle in a right triangle is the ratio of the opposite side (the height) to the adjacent side (the distance from the wall).

Given:
- Height = 15 feet
- Angle of inclination = 60°

We use the formula:

\[
\tan(\theta) = \frac{{\text{{opposite}}}}{{\text{{adjacent}}}}
\]

Substituting the given values:

\[
\tan(60^\circ) = \frac{15}{\text{{adjacent}}}
\]

Now let's solve for the adjacent side.The distance from the base of the ladder to the wall is approximately 8.66 feet.

Would you like further details or have any questions? Here are five related questions to explore:

1. What is the total length of the ladder in this scenario?
2. How would the distance change if the angle of inclination were different?
3. How do we calculate the hypotenuse of this right triangle?
4. Can you find the angle if the distance from the wall and height are known?
5. What other trigonometric functions can be used in this context?

**Tip:** Always make sure to use consistent units when applying trigonometric functions.

When a ladder leans against a wall, it reaches a height of 15 feet. The angle of incline is 60°. How far away from the wall is the base of the ladder?

Learn how to calculate the distance of a ladder's base from a wall when the height is 15 feet and the angle of incline is 60°. This problem demonstrates the application of the tangent function in trigonometry, suitable for students in Grades 9-11.

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