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Section 4.3

Section 4.3. Right Triangle Trigonometry. Complementary Angles:. Two angles that add up to 90 degrees. Ex. 37° Ex. Supplementary Angles:. Two angles that add up to 180 degrees. Ex. 59° Ex. Definitions of Trigonometry Functions. Opposite Hypotenuse Side

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Section 4.3

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  1. Section 4.3 Right Triangle Trigonometry

  2. Complementary Angles: • Two angles that add up to 90 degrees. • Ex. 37° • Ex.

  3. Supplementary Angles: • Two angles that add up to 180 degrees. • Ex. 59° • Ex.

  4. Definitions of Trigonometry Functions Opposite Hypotenuse Side Adjacent Side

  5. Ex 1. Find the value of side BC. • Given side AB = 12 and angle C = 40˚ A B C

  6. Ex 2. Find the value of side AC. • Given side AB = 12 and angle C = 40˚ A B C

  7. Ex 3. Find the value of side AB. • Given side AC = 25 and angle C = 32˚ A B C

  8. Ex 4. Find the value of side BC. • Given side AC = 51 and angle A = 23˚ A B C

  9. Definitions of Trigonometric Functions • Let θ be an angle in standard position with (x, y) a point on the terminal side of θ and r =

  10. Definitions of Trigonometric Functions • Let θ be an angle in standard position with (x, y) a point on the terminal side of θ and r = sinθ = cosθ = tanθ = cscθ = secθ = cotθ =

  11. Ex 5. Let (-5, -12) be a point on the terminal side of θ. Find sine, cosine, and tangent of θ.

  12. Ex 6. Let (-3, 4) be a point on the terminal side of θ. Find sine, cosine, and tangent of θ.

  13. Evaluating Trig Functions • ASTC • All Students Take Calculus. • An acronym used to determine which trigonometric functions are positive in each quadrant of a coordinate plane.

  14. Ex 7. Given sin θ = 7/24, Find cosine and tangent of θ.

  15. Ex 8. Given tan θ = -5/4 and cos θ < 0. Find sine and secant of θ.

  16. Ex 9. Given csc θ = 41/9, Find sine, cosine and tangent of θ.

  17. Angle of Elevation • An angle that measures from the horizontal upward to an object.

  18. Angle of Depression • An angle that measures from the horizontal downward to an object.

  19. Ex 10. A person at one end of a 230 ft bridge spots the river’s edge directly below the opposite end of the end of the bridge and finds the angle of depression to be 57˚. How far below the bridge is the river?

  20. Ex 11. An escalator from the ground floor to the second floor of a department store is 110 ft long and rises 32 ft vertically. What angle does the escalator make with the ground floor?

  21. Ex 12. The Leaning Tower of Pisa now stands 179 ft high, with an 84.9° angle of elevation. Find the real height of the Tower.

  22. Ex 13. The Camera crew on the ground is recording the act of a performer walking a tightrope stretched between two buildings. When the performer steps out onto the other end of the tightrope, the angle of elevation is 75˚. If the buildings are 30 m apart, how many meters above the ground is the performer?

  23. Ex 14. A person in an apartment building sights the top and bottom of an office building 500 ft away. The angle of elevation for the top of the office building is 23˚ and the angle of depression for the base of the building is 50˚. How tall is the office building?

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