1. Page 634 1)
b ≈ , c ≈ , C = 110° 3)
b ≈ , c ≈ , A = 14° 5)
a ≈ , c ≈ , A = 88° 7)
b ≈ , c ≈ , C ≈ 41.5°
17)
No Solution, b < c
19)
A1 ≈ °, C1 ≈ °, c ≈
A2 ≈ °, C2 ≈ °, c ≈
21)
No Solution, a < c
25)
b ≈ , c ≈ , C = 72°
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Area of a Triangle

2. Pre-Calculus AB PreAP/Dual, Revised ©2014
Area of a Triangle
Section 10.3
Pre-Calculus AB PreAP/Dual, Revised ©2014
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Area of a Triangle

3. The Area of a Triangle
The area of any triangle is given by A = ½bh, where b is its base and h is its height.
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Area of a Triangle

4. The Area of a Triangle
The area of any triangle is given by A = ½bh, where b is its base and h is its height.
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Area of a Triangle

5. Steps in Solving Area of a Triangle
Use this method in SAS Triangles
Draw a picture of triangle
Plug into the equation, A = ½ ac sin B
The calculator is in radian mode
Round to four decimal places
Label appropriately
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Area of a Triangle

6. Example 1
The area of triangle ABC if B = 55°, a = 34 feet, and c = 42 feet.
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Area of a Triangle

7. Example 2
The area of triangle ABC if a = 10 feet, b = 6 feet, and A = 42°
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Area of a Triangle

8. Example 2
The area of triangle ABC if a = 10 feet, b = 6 feet, and A = 42°
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Area of a Triangle

9. Your Turn
The area of triangle ABC if B = 27°, a = 4 meters, and b = 8 meters.
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Area of a Triangle

10. Question Determine the area of this triangle in centimeters
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Area of a Triangle

11. Question Determine the area of this triangle in centimeters
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Area of a Triangle

12. About Heron Determine the area of this triangle in centimeters
Physicist, mathematician, and engineer
Taught at the museum in Alexandria
Interests were more practical (mechanics, engineering, measurement) than theoretical
He is placed somewhere around 75 A.D. (±150)
Discovered areas of quadrilaterals, polygons from 3-12 sides, and circle and surface areas of 3-D objects
Heron’s Aeolipile was the first recorded steam engine. It was taken as being a toy but could have possibly caused an industrial revolution 2000 years before the original.
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Area of a Triangle

13. Proof Using Euclid’s Elements of Geometry:
The opposite angles of a cyclic quadrilateral sum to two right angles all derived from the Law of Cosines
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Area of a Triangle

14. Steps for Heron’s Formula
Applied to SSS triangles
Identify the semi-perimeter: 𝒔= 𝒂+𝒃+𝒄 𝟐
To find area, use the equation, 𝑨= 𝒔 𝒔−𝒂 𝒔−𝒃 𝒔−𝒄
Label correctly
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Area of a Triangle

15. Example 3
Find the area of the triangle whose sides have the length of 17 ft, 25 ft, and 26 ft
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Area of a Triangle

16. Example 3
Find the area of the triangle whose sides have the length of 17 ft, 25 ft, and 26 ft
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Area of a Triangle

17. Example 4
The distance “as the crow flies” from Los Angeles to New York is 2451 miles, from New York to Montreal is 331 miles, and from Montreal to Los Angeles is 2427 miles. What is the area of the triangular region having these three cities as vertices? (Ignore the curvature of the earth.)
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Area of a Triangle

18. Your Turn
The distance from Springfield to Shelbyville is 43 miles, Shelbyville to Capital City is 53 miles, and Capital City back to Springfield is 43 miles. Eventually, if you draw a shape, it makes an oblique triangle. Determine the area.
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Area of a Triangle

19. Assignment Page 634 9-16 all 2/24/2019 9:42 AM
Area of a Triangle