Geometry Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson

horizontal line of sight θ When you look UPWARDS…

Find the height of the kite if the string is 25 feet and the angle of elevation is 34 degrees. 25 feet 34 0 x

When you look downwards… horizontal line of sight θ

Find the height of the eyes of the man if he is 6.2 feet away from the basket and he makes an angle of 46 degrees. 6.2 feet 46 0 x

An observer from Point ___ looks at Point ___. A B C D E F

We can use trigonometric ratios to solve inaccessible distances. The angle of elevation OR depression is the angle the line of sight makes with the horizontal.

Ground Distance VS Vertical Distance VS Actual Distance Football Field Balloon Actual Distance Horizontal Distance Ground Distance Vertical Distance

Point A Point C Actual Distance from A to C TAKE NOTE: The actual distance is the SHORTEST distance between two objects. In a right triangle, it MAY NOT be the hypotenuse. TAKE NOTE: The actual distance is the SHORTEST distance between two objects. In a right triangle, it MAY NOT be the hypotenuse. Point B Actual Distance from A to B (along vertical)

Which trigonometric ratio is the most appropriate to use?

 A monument is 116 meters high and casts a shadow of 196 meters. What is the angle of elevation of the sun from the ground?

 To sight the top of the building 1000 feet away, you look up 24 o from the horizontal. What is the height of the building?

 If the angle of depression of the ship from the helicopter is 29 o, and the helicopter is 2640 feet away (actual distance) from the ship, what is the altitude of the helicopter?

 A person in a hot air balloon that is directly over a school building sights her house. The angle of depression is 42 o. The house is 1 mile from the school. Find the altitude of the balloon.

 An airplane pilot sights a life raft. The angle of depression is 26 0 and the plane’s altitude is 3 km. What is the plane’s actual distance from the raft? About 6.8 km

 An observer in an airport control tower sights and airplane at an angle of elevation of The pilot reports the plane’s altitude as 3.5 km. What is the airplane’s horizontal ground distance from the tower? About 5.6 km

 Two observers have an angle of elevation of 21 and 30 degrees to the tip of a mountain. If the two observers are 1000 meters apart, how high is the mountain?