MORE Trig Ratio Word Problems Draw a diagram for each problem (on another sheet of paper). Write the trig equation you will use to answer the question; solve. Round to the nearest tenth. 1. A guy wire is attached to a 100-foot tower that is perpendicular to the ground. The wire makes an angle of 55° with the ground. What is the length of the wire? 2. 2. In ∆XYZ, Z is a right angle. If sinX = ¾, find tanY. 3. A ship travels east from Port Lincoln 24 miles before turning north. When the ship becomes disabled and radios for help, the rescue boat needs to know the fastest route to the ship. The rescue boat navigator finds that the shortest route from Port Lincoln is 48 miles long. At what angle off of due east should the rescue boat travel to take the shortest route to the ship? 4. A jet airplane begins a steady climb of 15° and flies for two miles. What is the change in altitude in feet? 5. A surveyor is standing 100 meters from a bridge. She determines that the angle of elevation to the top of the bridge is 35°. The surveyor’s eye level is 1.45 meters above the ground. Find the height of the bridge.. 6. A ladder leaning against the side of a house forms an angle of 65° with the ground. The foot of the ladder is 8 feet from the building. Find the length of the ladder to the nearest foot. 7. To secure a 500-meter radio tower against high winds, guy wires are attached to a ring 5 meters from the top of the tower. The wires form a 15° angle with the tower. Find the distance from the tower to the guy wire anchor in the ground. 8. Mary is flying a kite o a 50-meter string. The string is making a 50° angle with the ground. How high above the ground is the kite? 9. Bill Owens is an architect designing a new parking garage for the city. The floors of the parking garage are to be 10 feet apart. The exit ramps between each pair of floors are to be 75 feet long. What is the measurement of the angle of elevation of each ramp? 10. From the top of a lighthouse, the angle of depression to a buoy is 25°. If the top of the lighthouse is 150 feet above sea level, find the distance from the buoy to the foot of the lighthouse. 11. At a certain time of day, the angle of elevation of the sun is 44°. Find the length of a shadow cast by a building 30 meters high. 12. A trolley car track rises vertically 40 feet over a horizontal distance of 630 feet. What is the angle of elevation of the track? 13. Danica is in the observation area of the Sears Tower in Chicago overlooking Lake Michigan. She sights two sailboats going due east from the tower. The angles of depression to the two boats are 42 degrees and 29 degrees. If the observation deck is 1,353 feet high, how far apart are the boats? 14. A 20-foot ladder leans against a wall so that the base of the ladder is 8 feet from the base of the building. What angle does the ladder make with the ground? 15. A 50-meter vertical tower is braced with a cable secured at the top of the tower and tied 30 meters from the base. What angle does the cable form with the vertical tower? 16. At a point on the ground 50 feet from the foot of a tree the angle of elevation to the top of the tree is 53°. Find the height of the tree. 17. From the top of a lighthouse 210 feet high the angle of depression of a boat is 27°find the distance from the boat to the foot of the lighthouse. The lighthouse was build at sea level. 18. Richard is flying a kite. The kite string makes an angle of 57° with the ground. If Richard is standing 100 feet from the point on the ground directly below the kite find the length of the kite string. 19. An airplane rises vertically 1000 feet over a horizontal distance of 1 mile. What is the angle of elevation of the airplane’s path? 20. Joe is standing on top of Marina Towers looking at the Leo Burnett World Headquarters building across the Chicago River. It is 880 feet between buildings. Joe finds the angle of elevation to the top of the Burnett building to be 8 degrees and the angle of depression to the ground level to be 20 degrees. How tall is the Burnett building to the nearest foot?
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