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Warm Up 1. Find w, y, and z. Give the answers in simplest radical form. Find each measure. 2. RT 3. UQ.

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Presentation on theme: "Warm Up 1. Find w, y, and z. Give the answers in simplest radical form. Find each measure. 2. RT 3. UQ."— Presentation transcript:

1 Warm Up 1. Find w, y, and z. Give the answers in simplest radical form. Find each measure. 2. RT 3. UQ

2 Objectives Find the area of sectors.
A sector is a fraction of a circle – it looks like a piece of pie or the curved piece of a circle if a triangle is taken out of the pie. Find arc lengths.

3

4 Write the degree symbol after m in the formula to help you remember to use degree measure not arc length. Helpful Hint

5 Example 1A: Finding the Area of a Sector
Find the area of each sector. Give answers in terms of  and rounded to the nearest hundredth. sector HGJ Use formula for area of sector. Substitute 12 for r and 131 for m. = 52.4 m2  m2 Simplify.

6 Example 1B: Finding the Area of a Sector
Find the area of each sector. Give answers in terms of  and rounded to the nearest hundredth. sector ABC Use formula for area of sector. Substitute 5 for r and 25 for m.  1.74 ft2  5.45 ft2 Simplify.

7 Example 2: Automobile Application
A windshield wiper blade is 18 inches long. To the nearest square inch, what is the area covered by the blade as it rotates through an angle of 122°? Use formula for area of sector. r = 18 in.  345 in2 Simplify.

8 Check It Out! Example 2 To the nearest square foot, what is the area that is watered as an irrigation sprinkler with diameter of 720 ft rotates through a semicircle? Use formula for area of sector. d = 720 ft, r = 360 ft  203,575 ft2 Simplify.

9 A segment of a circle is a region bounded by an arc and its chord.

10 Example 3: Finding the Area of a Segment
Find the area of segment LNM to the nearest hundredth. Step 1 Find the area of sector LNM. Use formula for area of sector. Substitute 9 for r and 120 for m. Simplify. = 27 cm2 Step 2 Find the area of ∆LNM. Draw altitude NO and use triangle ratios.

11 In a 30°-60°-90° triangle, the length of the leg opposite the 60° angle is √3 times the length of the shorter leg. Remember!

12 Example 3 Continued Find the area of segment LNM to the nearest hundredth. Step 3 area of segment = area of sector LNM – area of ∆LNM  cm2

13 Find the area of segment RST to the nearest hundredth.
Check It Out! Example 3 Find the area of segment RST to the nearest hundredth. Step 1 Find the area of sector RST. Use formula for area of sector. Substitute 4 for r and 90 for m. Simplify. = 4 m2 Step 2 Find the area of ∆RST. Note that it is an isosceles right triangle. = 8 m2

14 Check It Out! Example 3 Continued
Find the area of segment RST to the nearest hundredth. Step 3 area of segment = area of sector RST – area of ∆RST = 4 – 8  4.57 m2

15 Find the area of the segment if the central angle is 50º and the radius is 6”?
Draw diagram, label all given measures. Use trigonometry to find base and height of triangle! area of segment = area of sector – area of ∆

16 In the same way that the area of a sector is a fraction of the area of the circle, the length of an arc is a fraction of the circumference of the circle.

17 Example 4A: Finding Arc Length
Find each arc length. Give answers in terms of  and rounded to the nearest hundredth. FG Use formula for area of sector. Substitute 8 for r and 134 for m.  5.96 cm  cm Simplify.

18 Example 4B: Finding Arc Length
Find each arc length. Give answers in terms of  and rounded to the nearest hundredth. an arc with measure 62 in a circle with radius 2 m Use formula for area of sector. Substitute 2 for r and 62 for m.  0.69 m  2.16 m Simplify.

19 Extra Credit: 5% to quiz grade
Homework Page 767 Exercises 1-11, 41, 42 Quiz Tomorrow 11-1 thru 11-3 Extra Credit: 5% to quiz grade Page 771 Exercises 1-14, skip #3


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