
 Triangles Galore! 

Math 101.02
10 March, 1998
1.
Numbers 7, 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 shadow is 60 feet
tall, how tall is the tower?
Ans: 42.01245 ft
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? ?
Ans: 32.67949 ft
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?
Ans: 37.2º
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?
Ans: 7.471559º
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/minute?
Ans: 2125.5656 ft and 1062.7828 ft/minute
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.
Ans: 139 ft
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 28.5° (with your bank). After you walk 30 feet along the
bank (away from the rock), you notice that the angle is now 12°. How wide is the river?
Ans: 10.4790343 ft
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.
Ans: 2.662377 ft
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?
Ans: 0.8622869 km
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.
Ans: 5673.223453 ft
When the angle of elevation of the sun is 64°, a crooked telephone pole that is tilted at an angle of 12° past vertical directly away
from the sun casts a shadow 34 feet long on level ground. How long is the pole?
Ans: 49.636 ft
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?
Ans: 6.060393388 m
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?
Ans: 1664.279482 m
3.
4.
5.
6.
7.
8.
9.
10.
11.
13.
14.
15.