Applied Geometry -

Geometry Lesson 8 5 Angles of Elevation and Depression Objective: Solve problems involving angles of elevation and depression. Use angles of elevation and depression to find the distance between two objects. Elevation and Depression Angle of Elevation The angle formed by a horizontal line and an

observers line of sight to an object above the horizontal line Angle of Depression The angle formed by a horizontal line and an observers line of sight to an object below the horizontal line Be Careful! Angle of depression can be tricky! This is not an angle of depression!

Leah is meeting friends at the castle in the center of an amusement park. She sights the top of the castle at an angle of elevation of 38o. From the parks brochure, she knows that the castle is 190 feet tall. If Leah is 5.5 feet tall, about how far is she from the castle to the nearest foot? Sketch a picture 184.5 tan 38 x 184.5 x tan 38

x 236 ft The cross bar of a goalpost is 10 feet high. If a field goal attempt is made 25 yards from the base of the goal post 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? 10 + 1 11 x 75 11

tan x 75 11 tan x 75 1 x 8 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 42o and the helicopter is 18 feet above the water, what is the horizontal distance from the rescuers to this person to

the nearest foot? *have students draw picture on board 18 tan 42 x 18 x tan 42 x 20 ft A life guard is watching a beach from a line of sight

6 feet above the ground. She sees a swimmer at an angle of depression of 8o. How far away from the tower is the swimmer? x 6 feet 6 tan 8 x 6 x tan 8 x 43 ft

To estimate the height of a tree she wants removed, Mrs. Long sights the trees top at 70o angle of elevation. She then steps back 10 meters and sights the top at a 26o angle. If Mrs. Longs line of sight is 1.7 meters above the ground, how tall is the tree to the nearest meter? x tan 70 y Solve for a variable y tan 70 x x tan 26

10 y Solve for the same variable (10 y )(tan 26) x Cont Solve by system of equations y tan 70 x 2.16 tan 70 x (10 y )(tan 26) x x 5.93

(10 y )(tan 26) y tan 70 5.9 + 1.7 = 7.6 10 tan 26 y tan 26 y tan 70 The height is about 10 tan 26 y tan 70 y tan 26 8 meters. 10 tan 26 y (tan 70 tan 26) 10 tan 26 y tan 70 tan 26 y 2.16

Two buildings are sited from atop a 200meter skyscraper. Building A is sited at a 35o angle of depression, while Building B is sighted at a 36o angle of depression. How far apart are the two buildings to the nearest meter? 10 meters Homework Pg. 577 1 3 all, 4 20 EOE, 24, 28 48 E

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