To find the perimeter of the composite figure created by placing a sector of a circle on a triangle, follow these steps:
Given: Use 3.14 for π
1. **Calculate the Length of the Hypotenuse of the Right Triangle:**
- The sector of the circle forms an angle that corresponds to an angle in the triangle.
- The hypotenuse of the right triangle can be found using trigonometry, specifically the cosine function:
- Let's assume the radius of the circle is "r" and the central angle of the sector is "θ."
- The hypotenuse (side opposite the angle θ) of the right triangle can be calculated as: $r / \cos(θ)$
2. **Find the Arc Length of the Sector:**
- The arc length of the sector can be calculated using the formula: $2πr (θ / 360)$
- This formula represents the circumference of the circle multiplied by the fraction of the circle represented by the sector.
3. **Calculate the Perimeter of the Composite Figure:**
- The perimeter of the composite figure consists of the sum of the arc length of the sector, the length of the hypotenuse (side opposite the angle θ), and the sum of the other two sides of the triangle.
4. **Rounding:**
- Finally, round the perimeter to the nearest hundredth using the given value of π (3.14).
By following these steps and performing the calculations accurately, you can determine the perimeter of the composite figure created by placing a sector of a circle on a triangle.
