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 Triangles Galore!
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Math 101.01
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3, December, 1998
1. Numbers 6 – 9, 11, 17, and 23 from your text, page 382.
2. The angle of elevation of the top of a clock tower from the tip of its shadow (along
level ground) is 35°. If the tower is 60 feet tall, how long is its shadow?
3. A partially full oil storage tank is a cylinder 50 feet tall and 30 ft in diameter. From a
point on the top edge, the angle of depression of the surface of the oil on the opposite
side of the tank is 30°. What is the height of the oil in the tank?
4. A 12-foot ladder is leaning against the wall in a room. The top of the ladder is 7.25 ft
from the floor. What angle does the ladder make with the floor?
5. A golfer is about to hit her golf ball. It is 183 yards straight west from ball to the
hole. She hits the ball straight, but slightly offline. It ends up 24 yards straight north
of the hole. What is the angle between the intended line of flight and the actual line
of flight of the ball?
6. A plane flying level at 10,000 feet flies directly over an observer on the ground. Two
minutes later the angle of elevation on the plane from the observer is 78°. How many
feet has the plane flown in those 2 minutes? How fast is the plane flying in feet/sec?
7. As you stand on a bridge that is 100 feet above the water, you are looking at an
approaching barge. If the angle of depression of the front of the barge is 29° and the
angle of depression of the rear of the barge is 17.4°, find the length of the barge to the
nearest foot.
8. You wish to determine how far it is across a river with straight, parallel banks. As
you stand on one bank, you notice that your line of sight to a rock farther up the
opposite band makes an angle of 12° (with your bank). After you walk 30 feet along
the bank (away from the rock), you notice that the angle is now 28.5°. How wide is
the river?
9. A plane is flying at 480 mph on a level course directly away from you. At one time
you observe that its angle of elevation is 72°, while 5 minutes later it is 5°. How far
above the ground level where you are is the plane flying?
10. The angles of elevation of a balloon from two points A and B on level ground are
24.1° and 47.4°, respectively. If A and B are 8.4 miles apart and the balloon is
between A and B (and in the same vertical plane – for you smart alecks), approximate
the height of the balloon above the ground.
11. A ship is sailing on a straight course. A lighthouse is sighted ahead, and it is noted
that the angle between a line to the lighthouse and the ship's course is 27°. After
traveling 2.65 kilometers, the ship has gone past the lighthouse. The angle between
the ship's course and a line to the lighthouse is now 42°. How close did the ship come
to the lighthouse?
12. Suppose you are on level ground and you wish to measure the height of a mountain
above ground level. From some point A along the level ground you determine that
the angle of elevation of the peak is 54°, while from a point B, which is 200 feet
farther from the mountain, the angle of elevation of the peak is 52.7°. Find the
height.
13. A plane has crashed and activated an emergency transmitter. The signal is being
received by two rescue units, A and B. A is 8.63 kilometers due north of B. Using the
signal, the rescuers determine that the must take a course of 127.25° from A or 43.08°
from B to reach the plane. How far is each rescue unit from the plane?
14. When the angle of elevation of the sun is 64°, a crooked telephone pole that is tilted
at an angle of 12° directly away from the sun casts a shadow 34 feet long on level
ground. How long is the pole?
15. From a point 15 meters above level ground an observer measures the angle of
depression of an object on the ground as 68°. Approximately how far is the object
from the point on the ground directly beneath the observer?
16. In order to measure the height of a cloud cover, a spotlight is directed vertically
upward from the ground. From a point on level ground that is 1000 meters from the
spotlight, the angle of elevation of the light image on the clouds is 59°. How high are
the clouds?