HONORS GEOMETRY 8.5. Angle of Elevation/Depression Day One

Do Now: Find the missing variables

Homework Questions? Comments? Confusions? Concerns? ASK ASK ASK!

Angle Of Elevation The angle formed by a horizontal line and an observer’s line of sight to an object above the horizontal line.

Angle of Depression Is the angle formed by a horizontal line and an observer's line of sight to an object below the horizontal line.

Example One: At the circus, a person in the audience at ground level watches the high wire routine. A 5 foot, 6 inch tall acrobat is standing on a platform that is 25 feet off the ground. How far is the audience from the base of the platform if the angle of elevation from the audience member’s line of sight to the top of the acrobat is 27 degrees?

Example Two: At a diving competition, a 6-foot-tall diver stands atop the 32-foot platform. The front edge of the platform projects 5 feet beyond the ends of the pool. The pool itself is 50 feet in length. A camera is set up at the opposite end of the pool even with the pool’s edge. If the camera is angled so that its line of sight extends to the top of the diver’s head, what is the camera’s angle of elevation to the nearest degree?

Example Three: Suppose a tree 50 feet in height casts a shadow of length 60 feet. What is the angle of elevation from the end of the shadow to the top of the tree with respect to the ground?

You Try! Leah wants to see a castle in an amusement park. She sights the top of the castle at an angle of elevation of 38 degrees. She knows that the castle is 190 feet tall. If Leah is 5.5 feet tall, how far is she from the castle to the nearest foot? The cross bar of a goalpost is 10 feet high. If a field goal attempt is made from 25 yards from the base of the goalpost that clears the goal by 1 foot, what is the smallest angle of elevation at which the ball could have been kicked to the nearest degree? Hint: 1 yard = 3 feet

Example Four: Maria is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water and the angle of depression is 52 degrees, what is the horizontal distance from the seal to the cliff, to the nearest foot?

Example Five: Luisa is in a hot air balloon 30 feet above the ground. She sees the landing spot at an angle of depression of 34 degrees. What is the horizontal distance between the hot air balloon and the landing spot to the nearest foot?

Example Six: A bird is sitting on top of a lamppost. The angle of depression from the bird to the feet of an observer standing away from the lamppost is 35 degrees. The distance from the bird to the observer is 25 meters. How tall is the lamppost?

You Try! A search and rescue team is airlifting people from the scene of a boating accident when they observe another person in need of help. If the angle of depression to this other person is 42 degrees and the helicopter is 18 feet above the water, what is the horizontal distance from the rescuers to this person to the nearest foot? A lifeguard is watching a beach from a line of sight 6 feet above the ground. She sees a swimmer at an angle of depression of 8 degrees. How far away from the tower is the swimmer?

Practice Problems Try some on your own/in your table groups As always don’t hesitate to ask me questions if you are confused. Or talk to your table mates! They are your greatest resource!

Exit Ticket: A fan is seated in the upper deck of a stadium 200 feet away from home plate. If the angle of depression to the field is 62 degrees, at what height is the fan sitting?