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To calculate the length of chord \(k\), we can use the given information:

- The radius of the circle is \(30 \, \text{m}\).
- The area of the sector is \(816.81 \, \text{m}^2\).

### Step 1: Find the angle of the sector
The formula for the area of a sector is:
\[
\text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]
where:
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius.

We can rearrange this to solve for \(\theta\):
\[
\theta = \frac{\text{Area of sector} \times 360^\circ}{\pi r^2}
\]

Substituting the values:
\[
\theta = \frac{816.81 \times 360^\circ}{\pi \times 30^2}
\]

### Step 2: Calculate the length of chord \(k\)
The formula for the length of a chord is:
\[
\text{Length of chord } = 2r \sin\left(\frac{\theta}{2}\right)
\]
Once we find \(\theta\), we can use this formula to calculate \(k\).

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Do you have any questions or would you like a detailed breakdown? Here are five questions that expand on this topic:

1. What is the formula for the area of a sector?
2. How does the angle of the sector affect the length of a chord?
3. Can you use trigonometry to find the length of any chord in a circle?
4. What are some applications of chord length calculations in real life?
5. How would you calculate the area of a circle from the radius?

**Tip:** When solving problems involving sectors and chords, trigonometric functions are often essential for finding exact values!

Work out the length of chord k given the area of the sector is 816.81 m² and the radius is 30 m.

Discover the steps to calculate the length of a chord in a circle with a known sector area of 816.81 square meters and a radius of 30 meters. This guide uses trigonometric formulas to derive the angle of the sector and the chord length.

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