Mrs. King Pre-Calculus Applications of Right Triangles

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

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

Example: Solve  AB 106.2

Example: Solve  AB 106.2

Example: Solve  AB 106.2

Example: Solve  AB 106.2

Example: Solve  AB 106.2

Example: Solve  AB 106.2

Example: Solve  AB 106.2

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

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 . Find the height of the cloud.

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 . Find the height of the cloud.

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 . Find the height of the cloud.

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 . Find the height of the cloud.

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 . Find the height of the cloud.

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?

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?

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?

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?

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?  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?  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?  23’