Trig Ratio Word Problems by langkunxg

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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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