1. Mrs. King Pre-Calculus Applications of Right Triangles

2. Solving Right Triangles What does it mean to “solve” a right triangle?

3. Solving Right Triangles What does it mean to “solve” a right triangle? Find the lengths of all sides and the measures of all angles.

4. Example: Solve. 61.7  AB 106.2

5. Example: Solve. 61.7  AB 106.2

6. Example: Solve. 61.7  AB 106.2

7. Example: Solve. 61.7  AB 106.2

8. Example: Solve. 61.7  AB 106.2

9. Example: Solve. 61.7  AB 106.2

10. Example: Solve. 61.7  AB 106.2

11. Applications to Real World Situations “Angle of elevation” “Angle of depression”

12. Example #1 To measure cloud height at night, a vertical beam of light is directed on a spot on the cloud. From a point 135 ft away from the light source, the angle of elevation to the spot is found to be 67.35 . Find the height of the cloud.

13. Example #1 To measure cloud height at night, a vertical beam of light is directed on a spot on the cloud. From a point 135 ft away from the light source, the angle of elevation to the spot is found to be 67.35 . Find the height of the cloud.

14. Example #1 To measure cloud height at night, a vertical beam of light is directed on a spot on the cloud. From a point 135 ft away from the light source, the angle of elevation to the spot is found to be 67.35 . Find the height of the cloud.

15. Example #1 To measure cloud height at night, a vertical beam of light is directed on a spot on the cloud. From a point 135 ft away from the light source, the angle of elevation to the spot is found to be 67.35 . Find the height of the cloud.

16. Example #1 To measure cloud height at night, a vertical beam of light is directed on a spot on the cloud. From a point 135 ft away from the light source, the angle of elevation to the spot is found to be 67.35 . Find the height of the cloud.

17. Example #2 An aerial photographer who photographs farm properties for a real estate company has determined from experience that the best photo is taken at a height of approximately 475 ft and a horizontal distance of 850 ft from the farmhouse. What is the angle of depression from the plane to the house?

18. Example #2 An aerial photographer who photographs farm properties for a real estate company has determined from experience that the best photo is taken at a height of approximately 475 ft and a horizontal distance of 850 ft from the farmhouse. What is the angle of depression from the plane to the house?

19. Example #2 An aerial photographer who photographs farm properties for a real estate company has determined from experience that the best photo is taken at a height of approximately 475 ft and a horizontal distance of 850 ft from the farmhouse. What is the angle of depression from the plane to the house?

20. Example #3 A forest ranger at point A sights a fire directly south. A second ranger at point B, 7.5 miles east, sights the same fire at a bearing of S27  23’W. How far from A is the fire?

21. Example #3 A forest ranger at point A sights a fire directly south. A second ranger at point B, 7.5 miles east, sights the same fire at a bearing of S27  23’W. How far from A is the fire? 7.5 27  23’

22. Example #3 A forest ranger at point A sights a fire directly south. A second ranger at point B, 7.5 miles east, sights the same fire at a bearing of S27  23’W. How far from A is the fire? 7.5 27  23’

23. Example #3 A forest ranger at point A sights a fire directly south. A second ranger at point B, 7.5 miles east, sights the same fire at a bearing of S27  23’W. How far from A is the fire? 7.5 27  23’