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Additional Topics in Trigonometry

Additional Topics in Trigonometry. Use Law of Sines and the Law of Cosines to solve oblique triangles Find areas of Oblique triangles Represent vectors as directed line segments Perform mathematical operations on vectors Find direction angles of vectors

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Additional Topics in Trigonometry

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  1. Additional Topics in Trigonometry Use Law of Sines and the Law of Cosines to solve oblique triangles Find areas of Oblique triangles Represent vectors as directed line segments Perform mathematical operations on vectors Find direction angles of vectors Find the dot product of two vectors and use properties of the dot product Multiply and divide complex numbers written in trigonometric form Find powers and nth roots of complex numbers

  2. Law of Sines Oblique Triangles C C a b a h h b B A c c A B A is obtuse A is acute

  3. Given Two Angles and One Side -- AAS • For the trianlge Find the remaining angle and sides.

  4. Given Two Angles and One Side -- ASA • A pole tilts toward the sun at an angle from the vertical, and it casts a 22-foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is . How tall is the pole?

  5. Single Solution Case -- SSA • For the triangle a=22 inches, b=12 inches, and A=. Find the remaining side and angles.

  6. No-Solution Case -- SSA This contradicts the fact that . So, no triangle can be formed having sides a=15 and b=25 and an angle of

  7. Two-Solution Case --SSA , you can conclude that there are two possible triangles (because h<a<b). There are two angles . Find all measures of both angels

  8. Area of an Oblique Triangle • The area of any triangle is one-half the product of the lengths of two sides times the sine of their included angle. That is,

  9. Finding the Area of an Oblique Triangle • Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of .

  10. An application of the Law of Sines • The course for a boat race starts at point A and proceeds in the direction S to point B, then in the direction S E to point C, and finally back to A. Point C, lies 8 kilometers directly south of point A. Approximate the total distance of the race course. Larson p397

  11. Law of Cosines

  12. Heron’s Area Formula • Given any triangle with sides of lengths, a, b, and c, the area of the triangle is given by • Where

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