Given the angles of 70° and 40°, we can proceed with the calculations as follows:

### Problem Recap:
- **Angle at the base**: \( \theta = 40^\circ \)
- **Angle at the top of the slide**: \( 70^\circ \)
- **Height of the slide**: \( h = 2 \, \text{m} \)

### (a) Finding the Height of the Top of the Slide
This is simply the vertical height, which is given as \( 2 \, \text{m} \).

### (b) Finding the Length of the Slide
To find the length of the slide (the hypotenuse \( L \)), we can use trigonometry. Specifically, we use the sine function:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Here, the opposite side is the height of the slide, and the hypotenuse is the length of the slide.

\[
\sin(40^\circ) = \frac{2 \, \text{m}}{L}
\]

Solving for \( L \):

\[
L = \frac{2 \, \text{m}}{\sin(40^\circ)}
\]

Now, let's calculate the length \( L \):

\[
L \approx \frac{2 \, \text{m}}{0.6428} \approx 3.11 \, \text{m}
\]

### Summary:
- **Height of the slide**: \( 2 \, \text{m} \)
- **Length of the slide**: \( 3.11 \, \text{m} \)

Would you like more details or have any questions? Here are some related questions you might consider:

1. What if the height was different? How would the length change?
2. How can you calculate the base length of the ramp?
3. What trigonometric function would you use to find the base length?
4. What if the angle was 30° instead of 40°?
5. How do we ensure the stability of such a slide in real-world scenarios?

**Tip:** In any right triangle problem, knowing any two sides or one side and one angle allows you to solve for all unknowns using trigonometric identities.

Learn how to calculate the length of a slide using trigonometry with given angles of 70° and 40°. This problem involves finding the hypotenuse of a right triangle based on the height and angles provided. Suitable for high school students.

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