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The image contains two problems, both involving trigonometric relationships. I'll break down each problem for clarity and provide the steps to solve them.

### Problem 25:
**Statement:** "As shown in the accompanying figure, a pendulum of constant length \( L \) makes an angle \( \theta \) with its vertical position. Express the height \( h \) as a function of the angle \( \theta \)."

#### Solution:
- **Given:**
  - The pendulum length is \( L \).
  - The angle with the vertical is \( \theta \).
  - We need to express the height \( h \) as a function of \( \theta \).

- **Approach:**
  - The pendulum swings in a circular arc, and the vertical height \( h \) is the difference between the total length of the pendulum and the vertical component of the pendulum's length.
  - The vertical component of the pendulum length is \( L \cos(\theta) \).
  - Thus, the height \( h \) above the lowest point can be expressed as:
    \[
    h(\theta) = L - L \cos(\theta)
    \]
    Simplifying this gives:
    \[
    h(\theta) = L(1 - \cos(\theta))
    \]

### Problem 26:
**Statement:** "Express the length \( s \) of an arc of a circle with radius 10 cm as a function of the central angle \( \theta \) (see the accompanying figure)."

#### Solution:
- **Given:**
  - The radius of the circle is 10 cm.
  - The central angle is \( \theta \) (in radians).
  - We need to express the length of the arc \( s \) as a function of \( \theta \).

- **Approach:**
  - The formula for the length of an arc is:
    \[
    s = r \cdot \theta
    \]
    where \( r \) is the radius of the circle and \( \theta \) is the central angle in radians.
  - Substituting the given radius:
    \[
    s(\theta) = 10 \cdot \theta
    \]
  - So, the length of the arc is directly proportional to the angle \( \theta \) in radians.

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Do you have any questions or would you like further details on any of the steps?

### Related Questions:
1. How would the formula for height \( h(\theta) \) change if the pendulum is on an inclined plane?
2. What happens to the height \( h(\theta) \) when \( \theta \) is \( 90^\circ \)?
3. How can you express the length of an arc if the angle \( \theta \) is given in degrees instead of radians?
4. If the radius of the circle in Problem 26 were doubled, how would that affect the arc length \( s(\theta) \)?
5. How would you find the angle \( \theta \) if you were given the height \( h \) in Problem 25?

### Tip:
Always ensure that angles are in the correct units (radians or degrees) when applying trigonometric formulas, especially in problems involving circles or periodic functions.

Problem 25: As shown in the accompanying figure, a pendulum of constant length L makes an angle θ with its vertical position. Express the height h as a function of the angle θ. Problem 26: Express the length s of an arc of a circle with radius 10 cm as a function of the central angle θ (see the accompanying figure).

This page explains how to express the height of a pendulum and the length of an arc as functions of the angle θ. The pendulum height formula involves trigonometric concepts, while the arc length formula demonstrates key principles in geometry. Suitable for high school students in grades 9-12.

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