It looks like you've uploaded two images with math problems. Let's tackle them step by step:

First Problem:

A pendulum with a length of 18 cm swings through an angle of 87°. The goal is to find the distance the pendulum end travels when it swings through this angle.

To solve this:

1. Use the formula for arc length:
   $\text{Arc length} = \theta \times r$ where $\theta$ is the angle in radians and $r$ is the radius (or length of the pendulum).

2. Convert the angle from degrees to radians: $\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180}$ $\theta_{\text{radians}} = 87^\circ \times \frac{\pi}{180} \approx 1.519 \text{ radians}$

3. Calculate the arc length: $\text{Arc length} = 1.519 \times 18 \, \text{cm} \approx 27.3 \, \text{cm}$

Second Problem:

A sector of a circle has a diameter of 70 cm and a central angle of 29°. The task is to find the length of the minor arc AB.

1. Find the radius:
   $\text{Radius} = \frac{\text{Diameter}}{2} = \frac{70}{2} = 35 \, \text{cm}$

2. Convert the angle from degrees to radians: $\theta_{\text{radians}} = 29^\circ \times \frac{\pi}{180} \approx 0.507 \text{ radians}$

3. Calculate the arc length using the formula: $\text{Arc length} = \theta \times r$ $\text{Arc length} = 0.507 \times 35 \, \text{cm} \approx 17.7 \, \text{cm}$

Summary:

• Pendulum arc length: 27.3 cm
• Minor arc length: 17.7 cm

Would you like a more detailed explanation or have any follow-up questions?

Related Questions:

1. How does the length of a pendulum affect the arc length?
2. What other formulas can be used to find the length of an arc in different situations?
3. How would the result change if the angle was 180° for the pendulum?
4. How do you derive the formula for the arc length of a circle?
5. What is the relationship between the central angle and the radius in a sector?

Tip: Remember, when converting degrees to radians, multiply by $\frac{\pi}{180}$.