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4-1 Right Triangle Trigonometry

4-1 Right Triangle Trigonometry. Chapter 4 Trigonometric Functions. Recall how to find the missing values in each figure (angles and sides). 15 x y 60 ° 45° 6

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4-1 Right Triangle Trigonometry

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  1. 4-1 Right Triangle Trigonometry Chapter 4 Trigonometric Functions

  2. Recall how to find the missing values in each figure (angles and sides) 15 x y 60° 45° 6 b 7 a 13 6.5√3

  3. 1. Finding the Values of Trigonometric Ratios (for acute angles) The ratios of the sides of right triangles can be used to define trigonometric ratios

  4. Example 1: Find the sine, cosine, and tangent for ∠T U 15 V 17 T

  5. The ratios of the sides of right triangles can be used to define trigonometric ratios

  6. Example 2: Find the exact values of the six trigonometric functions of θ. C 65 33 θ A 56 B

  7. Example 3 • If sin θ = , find the exact values of the five remaining trigonometric functions

  8. We can use these principles to find missing sides of triangles We could find the missing side length of this triangle. 18 42° x

  9. Try these. • Example 4: Find x. 53° x 15 • Example 5: Find x 9 x 21°

  10. Sports Example A competitor in a hiking competition must climb up the inclined course as shown to reach the finish line. Determine the distance in feet that the competitor must hike to reach the finish line. (Photo not to scale) Finish x 48° 1 mile

  11. Assignment • P. 227, 1 – 17 odds, 19 – 26 all • This is not a good assignment to skip. • Begin this section with a strong foundation in the basics. • This lesson is the basics!

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