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Section 9-1

Section 9-1. Solving Right Triangles. Solving a Triangle. In chapter 7 we defined the trigonometric functions in terms of coordinates of points on the circle. In this chapter, we will shift our emphasis to triangles. Solving a Triangle.

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Section 9-1

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  1. Section 9-1 Solving Right Triangles

  2. Solving a Triangle • In chapter 7 we defined the trigonometric functions in terms of coordinates of points on the circle. In this chapter, we will shift our emphasis to triangles.

  3. Solving a Triangle • When certain parts (sides and angles) of a triangle are known, you can use trigonometric relationships to find the unknown parts. This is called solving the triangle.

  4. Trigonometric Functions • The right triangles shown on p. 331 both have an acute angle of measure Θ and are similar. Therefore the lengths of the corresponding sides are proportional. hypotenuse opposite θ adjacent

  5. Trigonometric Functions • This gives us the following equations:

  6. OPP TAN= ADJ OPP SIN= HYP ADJ COS= HYP SohCahToa

  7. Label the triangle

  8. Trigonometric Functions • By the reciprocal relationships we also have:

  9. Example • In ∆ABC, A = 90°, a = 29 and b = 21. Find c, B and C.

  10. Example • A rhombus with perimeter 40 cm has a 70° angle. Find the lengths of its diagonals.

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