The proper angle for a ladder is about 75° from the ground. Suppose you have a 25 foot ladder. How high can it reach?


To determine how high a 25-foot ladder can reach when placed at a 75° angle from the ground, we can use trigonometry. Specifically, we will apply the sine function, which relates the angle of the ladder to its height and length.

### Formula:
\[
\sin(\theta) = \frac{\text{height}}{\text{ladder length}}
\]
Where:
- \(\theta = 75^\circ\) (the angle between the ladder and the ground)
- Ladder length = 25 feet

Rearranging the formula to solve for the height:
\[
\text{height} = \text{ladder length} \times \sin(\theta)
\]
Substituting the values:
\[
\text{height} = 25 \times \sin(75^\circ)
\]

Let me calculate that.The ladder can reach a height of approximately 24.15 feet when placed at a 75° angle from the ground.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. What would the height be if the ladder was placed at a 60° angle instead?
2. How far from the wall should the base of the ladder be placed?
3. What is the horizontal distance from the base of the ladder to the wall?
4. How does the height change if the ladder is 30 feet long?
5. Can the sine function be applied to other real-world scenarios like ramps or slopes?

**Tip**: Always ensure that a ladder is properly secured and placed at a safe angle for stability, usually between 70-75°.

The proper angle for a ladder is about 75° from the ground. Suppose you have a 25 foot ladder. How high can it reach?

Learn how to determine the height a 25-foot ladder can reach when placed at a 75° angle using trigonometry. This guide covers the sine function and trigonometric ratios, making it suitable for students in Grades 9-10.

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