Right triangle problems
- 1. Solving Right Triangle Problems Mathematics 4 October 27, 2011 1 of 14
- 2. Right triangles and the unit circle Sine, cosine, and the unit circle: 2 of 14
- 3. Right triangles and the unit circle Right triangles beyond the unit circle: 3 of 14
- 4. Right triangles and the unit circle We can relate the two right triangles by similarity: sin θ cos θ 1 = = opp adj hyp 4 of 14
- 5. Right triangles and the unit circle We can relate the two right triangles by similarity: sin θ cos θ 1 = = opp adj hyp Isolating the trigonometric functions: 4 of 14
- 6. Right triangles and the unit circle We can relate the two right triangles by similarity: sin θ cos θ 1 = = opp adj hyp Isolating the trigonometric functions: opp sin θ = hyp 4 of 14
- 7. Right triangles and the unit circle We can relate the two right triangles by similarity: sin θ cos θ 1 = = opp adj hyp Isolating the trigonometric functions: adj cos θ = hyp 4 of 14
- 8. Right triangles and the unit circle We can relate the two right triangles by similarity: sin θ cos θ 1 = = opp adj hyp Isolating the trigonometric functions: opp tan θ = adj 4 of 14
- 9. Solve the right triangles given the following parts: 1. α = 17o , a = 135 5 of 14
- 10. Solve the right triangles given the following parts: 1. α = 17o , a = 135 β = 73o , c = 461.7, b = 441.6 5 of 14
- 11. Solve the right triangles given the following parts: 1. α = 17o , a = 135 β = 73o , c = 461.7, b = 441.6 2. a = 64.5, b = 57.2 5 of 14
- 12. Solve the right triangles given the following parts: 1. α = 17o , a = 135 β = 73o , c = 461.7, b = 441.6 2. a = 64.5, b = 57.2 α = 48.4o , β = 41.6o , c = 86.2 5 of 14
- 13. Applications of Right Triangle Solutions: Definition of terms: Angle of Elevation Angle of Depression 6 of 14
- 14. Applications of Right Triangle Solutions: Example 1 Find the length of the pole, and the distance of the pole from the building. 7 of 14
- 15. Applications of Right Triangle Solutions: Example 2 Find the distance across the river (indicated by P Q) 8 of 14
- 16. Applications of Right Triangle Solutions: Example 3: The problem needs to be illustrated first How high is a building whose horizontal shadow is 50 meters when the angle of elevation of the sun is 65 degrees? 9 of 14
- 17. Applications of Right Triangle Solutions: Example 4 An 18-meter ladder leaning up against a building makes a 70 degree angle with the ground. How far up the building does the ladder touch? 10 of 14
- 18. Applications of Right Triangle Solutions: Example 5 A 36-foot ladder is used to reach the top of a 28-foot wall. If the ladder extends 2 feet past the top of the wall, find its inclination to the horizontal. 11 of 14
- 19. Applications of Right Triangle Solutions: Definition of Terms: Course - angle measured in Bearing - angle measured in degrees clockwise from the north degrees clockwise from the north to the direction a ship is traveling. of Ship A to the line segment connecting Ship A and Ship B. 12 of 14
- 20. Applications of Right Triangle Solutions: Example 6 Two ships leave a port at the same time. The first ship sails on a course of 25 degrees at 15 knots (1 knot = 1 mi/hr) while the second ship sails on a course of 115 degrees at 20 knots. Find after two hours (a) the distance between the ships, and (b) the bearing from the first ship to the second and (c) the bearing of the second ship to the first. 13 of 14
- 21. Any questions? 14 of 14