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# Right triangle problems

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### Right triangle problems

1. 1. Solving Right Triangle Problems Mathematics 4 October 27, 20111 of 14
2. 2. Right triangles and the unit circleSine, cosine, and the unit circle: 2 of 14
3. 3. Right triangles and the unit circleRight triangles beyond the unit circle: 3 of 14
4. 4. Right triangles and the unit circle We can relate the two right triangles by similarity: sin θ cos θ 1 = = opp adj hyp4 of 14
5. 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. 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 = hyp4 of 14
7. 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 = hyp4 of 14
8. 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 = adj4 of 14
9. 9. Solve the right triangles given the following parts:1. α = 17o , a = 135 5 of 14
10. 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. 11. Solve the right triangles given the following parts:1. α = 17o , a = 135 β = 73o , c = 461.7, b = 441.62. a = 64.5, b = 57.2 5 of 14
12. 12. Solve the right triangles given the following parts:1. α = 17o , a = 135 β = 73o , c = 461.7, b = 441.62. a = 64.5, b = 57.2 α = 48.4o , β = 41.6o , c = 86.2 5 of 14
13. 13. Applications of Right Triangle Solutions:Deﬁnition of terms: Angle of Elevation Angle of Depression 6 of 14
14. 14. Applications of Right Triangle Solutions:Example 1Find the length of the pole, and the distance of the pole from thebuilding. 7 of 14
15. 15. Applications of Right Triangle Solutions:Example 2Find the distance across the river (indicated by P Q) 8 of 14
16. 16. Applications of Right Triangle Solutions:Example 3: The problem needs to be illustrated ﬁrstHow high is a building whose horizontal shadow is 50meters when the angle of elevation of the sun is 65degrees? 9 of 14
17. 17. Applications of Right Triangle Solutions:Example 4An 18-meter ladder leaning up against a buildingmakes a 70 degree angle with the ground. How far upthe building does the ladder touch?10 of 14
18. 18. Applications of Right Triangle Solutions:Example 5A 36-foot ladder is used to reach the top of a 28-footwall. If the ladder extends 2 feet past the top of thewall, ﬁnd its inclination to the horizontal.11 of 14
19. 19. Applications of Right Triangle Solutions:Deﬁnition of Terms: Course - angle measured in Bearing - angle measured indegrees clockwise from the north degrees clockwise from the northto the direction a ship is traveling. of Ship A to the line segment connecting Ship A and Ship B.12 of 14
20. 20. Applications of Right Triangle Solutions:Example 6Two ships leave a port at the same time. The ﬁrstship sails on a course of 25 degrees at 15 knots (1knot = 1 mi/hr) while the second ship sails on acourse of 115 degrees at 20 knots. Find after twohours (a) the distance between the ships, and (b) thebearing from the ﬁrst ship to the second and (c) thebearing of the second ship to the ﬁrst.13 of 14
21. 21. Any questions?14 of 14