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Trigonometry for Right Triangles: Solving Unknown Sides & Angles

Learn to use trigonometry to find missing sides or angles of right triangles. Explore definitions and practical applications, solving triangles with given measurements and angles. Practice calculations and angle measurements for various scenarios.

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Trigonometry for Right Triangles: Solving Unknown Sides & Angles

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  1. Lesson 9-1 Solving Right Triangles

  2. Objective:

  3. Objective: • To use trigonometry to find unknown sides or angles of a right triangle.

  4. All the work we have been doing thus far leads us into using trigonometry to solve right triangles.

  5. All the work we have been doing thus far leads us into using trigonometry to solve right triangles. If you go back to the unit circle, it was basically set up there.

  6. Definitions

  7. Definitions

  8. Definitions

  9. Definitions

  10. Definitions If we look at this more closely, the y-value represents the length of the leg opposite θ and the radius represents the length of the hypotenuse.

  11. Thus,

  12. Thus,

  13. Thus,

  14. Thus,

  15. For the right triangle JKL shown, find the value of k to three significant digits. ( l = 40, Angle L = 280)

  16. The safety instructions for a 20 ft. ladder indicate the ladder should not be inclined at more than a 700 angle with the ground. Suppose the ladder is leaned against a house at this angle. Find:

  17. The safety instructions for a 20 ft. ladder indicate the ladder should not be inclined at more than a 700 angle with the ground. Suppose the ladder is leaned against a house at this angle. Find: A) The distance x from the base of the house to the foot of the ladder.

  18. The safety instructions for a 20 ft. ladder indicate the ladder should not be inclined at more than a 700 angle with the ground. Suppose the ladder is leaned against a house at this angle. Find: A) The distance x from the base of the house to the foot of the ladder. B) The height y reached by the ladder.

  19. The highest tower in the world is in Toronto, Canada which is 553 m high. An observer at point A, 100 m from the center of the tower’s base, sights the top ofthe tower. The angle of elevationis A.

  20. The highest tower in the world is in Toronto, Canada which is 553 m high. An observer at point A, 100 m from the center of the tower’s base, sights the top ofthe tower. The angle of elevationis A. • Find the measure of this angle to the nearest tenth of a degree.

  21. A triangle has sides of lengths 8, 8, and 4.

  22. A triangle has sides of lengths 8, 8, and 4. • Find the measures of the angles of the triangle to the nearest tenth of a degree.

  23. Assignment:Pgs. 334-338 1-27 odd, 31-37 odd

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