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The question asks to find the length of the chord \( AB \) in a circle with center \( O \), radius \( 8 \) cm, and angle \( \angle AOB = 2.4 \) radians.

### Solution:

Given:

- Radius of the circle, \( r = 8 \) cm.
- Central angle \( \angle AOB = 2.4 \) radians.

The formula for the length of a chord \( AB \) in terms of the radius \( r \) and the central angle \( \theta \) in radians is:

\[
AB = 2r \sin\left(\frac{\theta}{2}\right)
\]

Substitute the given values:

\[
AB = 2 \times 8 \times \sin\left(\frac{2.4}{2}\right)
\]

Simplifying:

\[
AB = 16 \sin(1.2)
\]

Calculating \( \sin(1.2) \approx 0.932 \):

\[
AB \approx 16 \times 0.932 = 14.912 \, \text{cm}
\]

So, the length of \( AB \) is approximately **14.912 cm**.

Would you like further details or have any questions on this solution?

### Related Questions:

1. How do you find the arc length subtended by the chord \( AB \)?
2. What is the area of the sector \( AOB \) for the given values?
3. If the radius is doubled, how would the length of \( AB \) change?
4. Can you find the perpendicular distance from \( O \) to \( AB \)?
5. What would be the length of \( AB \) if \( \angle AOB \) was measured in degrees?

**Tip**: When solving problems involving circles, it’s often useful to express angles in radians, as many circle properties and formulas use radians naturally.

The diagram shows a metal plate made by removing a segment from a circle with center O and radius 8 cm. The line AB is a chord of the circle and angle AOB = 2.4 radians. Find the length of AB.

Solve the problem of finding the length of chord AB in a circle with radius 8 cm and central angle 2.4 radians. This involves applying the chord length formula using trigonometry. Suitable for high school students in Grades 9-12.

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