WORD PROBLEMS
Name_________________________
An angle of elevation is ____________________________________________________
An angle of depression is ___________________________________________________
For the problems below, draw a sketch of the situation. The sketches should be right triangles.
Example: From a 60 foot observation tower on the coast, a Coast Guard officer sights a boat in the water.
The angle of depression to the boat is 4.5º. How far is the boat from the shore line?
Example: You are standing 75 meters from the base of the Jin Mao Building in Shanghai, China. You
estimate that the angle of elevation to the top of the building is 80º. What is the approximate height of
the building?
Homework
1. The angle of elevation to a helicopter from a ship is 35°. The altitude of the helicopter is 2800
meters. How far is it from a buoy, directly below the helicopter, to the ship?
2. A person 1320 feet from a television tower, sights its top. The angle of elevation is 24°. How tall is
the tower?
3. A person in a hot-air balloon that is directly over a school sights her home. The angle of
depression is 42°. The house is one mile from the school. Find the altitude of the balloon (in feet).
4. The length of a guy-wire supporting a radio tower is 175 feet. The angle of elevation to the top of
the tower from the foot of the guy-wire is 65°. How tall is the tower?
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A guy-wire or guy-rope is a tensioned cable designed to add stability to structures (frequently ship
masts, radio masts, wind turbines, utility poles, and tents). One end of the cable is attached to the
structure, and the other is anchored to the ground at a distance from the structure's base. They are
often configured radially (equally spaced about the structure) in trios, quads (pairs of pairs) or other
sets. This allows the tension of each guy-wire to offset the others. For example, roof antennas are
sometimes held up by three guy-wires. http://en.wikipedia.org/wiki/Guy-wire
5. A ramp is 120 feet long and rises vertically 15 feet. Find the angle of elevation of the ramp.
6. A tower 150 feet high casts a shadow 200 feet long. Find the angle of elevation to the sun.
7. A person on a bridge sights a boat at an angle of depression of 6°. The bridge is 96 feet above the
water. If the boat is traveling 440 feet per minute, about how long will it take the boat to reach the
bridge?
8. An observer at the top of a 50 meter high lighthouse sights two ships approaching, one behind the
other. The angles of depression are 36° and 25°. Find the distance between the ships.
9. A navy reconnaissance plane is at 3000 feet as it passes over its carrier. At that instant, the copilot
sights a submarine. Find the distance from the aircraft carrier to the submarine if the angle of
depression of the submarine is 32°.
10. An uphill street rises 95 meters through a distance of 315 meters. What is the measure of the
incline?
11. A student looks out of a second-story window and sees the top of a flagpole at an angle of elevation
of 22°. The student is 18 feet above the ground and 15 feet from the flagpole. Find the height of
the flagpole.