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Lesson 9-2

Lesson 9-2. The Area of a Triangle. Objective:. Objective:. To find the area of a triangle given the lengths of two sides and the measure of the included angle.

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Lesson 9-2

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  1. Lesson 9-2 The Area of a Triangle

  2. Objective:

  3. Objective: To find the area of a triangle given the lengths of two sides and the measure of the included angle.

  4. By using right triangle trigonometry, we can now make a few adjustments and create many new formulas to help us findspecific information about triangles.

  5. For instance, the area of a triangle (k = ½ bh) is how we have known to find the area of any triangle but most of the time the height of a triangle is not that easy to find. It had to be given to us or we would have been in trouble.

  6. But, we can now use trigonometry to make a few adjustments: B a h C A b

  7. But, we can now use trigonometry to make a few adjustments: B a h C A b In triangle ABC shown:

  8. But, we can now use trigonometry to make a few adjustments: B a h C A b In triangle ABC shown:

  9. But, we can now use trigonometry to make a few adjustments: B a h C A b In triangle ABC shown: or

  10. But, we can now use trigonometry to make a few adjustments: B a h C A b So, by substitution:

  11. But, we can now use trigonometry to make a few adjustments: B a h C A b So, by substitution:

  12. But, we can now use trigonometry to make a few adjustments: B a h C A b The formula could be also written as:

  13. But, we can now use trigonometry to make a few adjustments: B a h C A b The formula could be also written as:

  14. But, we can now use trigonometry to make a few adjustments: B a h C A b But in theory, what you need to realize is that to find the area of a triangle all you need is two sides and the included angle.

  15. But, we can now use trigonometry to make a few adjustments: B a h C A b Because, k = ½ (one side) (another side) (sine of included angle)

  16. Two sides of a triangle have lengths of 7 cm and 4 cm. The angle between the sides measures 730. Find the area of the triangle.

  17. The area of Δ PQR is 15. If p = 5 and q = 10, find all possible measures of < R.

  18. Find the exact area of a regular hexagon inscribed in a unit circle. Then approximate the area to three significant digits.

  19. Adjacent sides of a parallelogram have lengths 12.5 cm and 8 cm. The measure of the included angle is 400. Find the area of the parallelogram to three significant digits.

  20. Assignment:Pgs. 342-343 1-19 odd, 18, 20, 22, 28, 30

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