Angle of Elevation and Depression
Angle of Elevation and Depression 1. An airplane flying at an altitude of 15000 feet starts its descent when it is 10 miles from the runway, measured horizontally. Draw a diagram showing the airplane and the runway. Then calculate the angle of depression that the airplane needs to use as it starts its descent. (1 mile = 5280 feet). 2. According to a Chinese legend from the Han dynasty (206 B.C.E.–220 C.E.), General Han Xin flew a kite over the palace of his enemy to determine the distance between his troops and the palace. If the general let out 800 meters of string and the kite was flying at a 35° angle of elevation, how far away was the palace from General Han Xin’s position? 3. Benny is flying a kite directly over his friend Frank, who is 125 meters away. When he holds the kite string down to the ground, the string makes a 39° angle with the level ground. How high is Benny’s kite? 4. The angle of elevation from a ship to the top of a 42-‐meter lighthouse on the shore measures 33°. How far is the ship from the lighthouse? (Assume the horizontal line of sight meets the bottom of the lighthouse.) 5. A lighthouse 55 meters above sea level spots a distress signal from a sailboat. The angle of depression to the sailboat measures 21°. How far away is the sailboat from the base of the lighthouse? 6. A ladder 7 m long stands on level ground and makes a 73° angle with the ground as it rests against a wall. How far from the wall is the base of the ladder? 7. To see the top of a building 1000 feet away, you look up 24° from the horizontal. What is the height of the building? 8. A salvage ship’s sonar locates wreckage at a 12° angle of depression. A diver is lowered 40 meters to the ocean floor. How far does the diver need to walk along the ocean floor to the wreckage? 9. A guy wire is anchored 12 feet from the base of a pole. The wire makes a 58° angle with the ground. How long is the wire?