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 find specific 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: h A B C a b

7. h A B C a b In triangle ABC shown:

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

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

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

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

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

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

14. But, we can now use trigonometry to make a few adjustments: h A B 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: h A B 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 73 0. 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 40 0. Find the area of the parallelogram to three significant digits.

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