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developed by Vicki Borlaug Walters State Community College Summer 2008 Word Problems: Using Trigonometric Functions to find Angles

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Example 1.) A scuba diver is on the top of the water and is going to dive in a straight line to a treasure chest on the ocean floor. The floor of the ocean is flat and the water is 70 feet deep. The treasure chest sits 200 feet away from a point on the ocean floor that is directly below the diver. a.) Find the angle of depression the scuba diver must dive to swim directly to the treasure chest. b.) Suppose that first the diver swims towards the treasure chest on the surface for 95 feet and then dives in a straight line to the treasure chest. Find the angle of depression the diver must make to reach the treasure chest with this approach. Not drawn to scale. Question developed by V. Borlaug WSCC, 2008

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Not drawn to scale. Question developed by V. Borlaug WSCC, 2008 Example 2.) A crane has a 65 foot long arm. The base of the arm is 100 feet high and the tip of the arm is 137 feet high. Find the angle of elevation the crane’s arm.

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Location: Paris, France Architect: Gustave Eiffel Constructed: 1887-1889, designed to be the entrance arch for the World’s Fair, the Exposition Universelle Some History: In 1944 during WW II when the Allies were approaching France, Hitler ordered General Dietrich von Choltitz to demolish the tower. Von Choltitz disobeyed the order. Example 3.) The roof of the Eiffel Tower is 301 meters high. The antenna that sits on the roof is 24 meters tall. A man is standing on the ground 200 meters away from the base of the tower. His eyes are 1.75 meters above the ground. a.) Find the angle of elevation required for the man to look directly at the roof of the Eiffel Tower. b.) Find the angle of elevation required for the man to look directly at the top of the antenna on the Eiffel Tower. http://en.wikipedia.org/wiki/Eiffel_Tower Question developed by V. Borlaug WSCC, 2008

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Example 4.) A Navy fighter jet is lined up to land on an aircraft carrier. The fighter jet is 6000 feet due east of the aircraft carrier. The fighter jet is 2000 feet above sea level and the flight deck of the carrier is 85 feet above sea level. Find the angle of depression the fighter jet must use to approach the deck of the carrier in a straight line approach. Not drawn to scale.

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Example 5.) A helicopter sits on the ground 850 feet due east of a motion picture camera. Initially the camera is pointed directly at the helicopter on the ground. The helicopter will ascend vertically 700 feet, fly due west for 1050 feet, and then hover. The camera man will keep the camera pointed at the helicopter during the flight. Find the angle the camera will need to make in order to follow the flight of the helicopter to its hovering position. (You may assume the camera lens is at ground level.) Not drawn to scale. Question developed by V. Borlaug WSCC, 2008

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Example 6.) A five foot gate is in the middle of a picket fence. Find the angle the gate must swing open so that its outer edge is three (perpendicular) feet from the original fence line. Yard Sale

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Example 7.) In a sailboat race the boats must travel east, turn counterclockwise around a first buoy, and then head towards a second buoy. The second buoy is 200 feet west and 425 feet north of the first buoy. A sailboat is headed due east towards the first buoy. How many degrees must the sailboat change its heading in order to go counterclockwise around the first buoy and head toward the second buoy? Not drawn to scale. Question developed by V. Borlaug WSCC, 2008 angle θ

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Example 8.) A tow truck has a 12 foot arm that is attached to the truck bed 4.5 feet above ground level. A car has a bumper 2.1 feet above ground level. A chain with a hook drops vertically 6.3 feet from the end of the arm and is attached to the bumper. Find the arm’s angle of elevation of the tow truck’s arm.

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Example 9: A boat is tied with a rope from its bow to an edge of a dock. The rope is stretched tightly so that it is forms in a straight line. The bow of the boat is 6.9 feet above the water line and the dock is 4.2 feet above the water line. The bow of the boat is 3.8 horizontal feet from the edge of the dock. a.) Draw a picture to represent this situation and label with the drawing with the appropriate numbers. b.) Find the angle of depression of the rope. c.) Find the length of the rope. (Use two decimal places in your answer and include the units.) d.) Suppose a sailor pulls in the rope so that its length is reduced by 1 ¾ feet. Assume that the rope still forms a straight line. Draw a picture to represent this situation and find the new angle of depression. (Think about what numbers in your original drawing have changed and what numbers have stayed the same.)

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The end!

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x°x° 200 70 1) B) 95105 70 y°y° A)

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100 37 65 2) x°x°

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x° y° 301 24 200 3) A)B)

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4) 1915 85 2000 6000 x°

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700 850200 700 850 x°c H 5)

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3 x° 5 6)

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7) 200 425 180-x x°

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8) 4.5 2.1 6.3 3.9 12 x°

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9) (6.9 - 4.2)= 2.7 3.8 x° A) B) C)

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Discuss how the following sequence of diagrams allows us to determine the height of the Eiffel Tower without actually having to climb it. Trigonometry.

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