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Algebra & Analytic Geometry
Trigonometry – Word Problem Applications
Name & Date
1) An airplane is flying in a horizontal straight line towards an airport. Find its altitude at the moment when
the angle of depression is 6 and the plane is 100 miles away from its destination.
2) Gertie the gopher is looking at a tree that is 100 feet away from her nest. If the angle of elevation between
Gertie’s nest and the top of the tree is 23°, how tall is the tree?
3) A plane is 30,000 feet off of the ground when it begins its approach to the runway. How far is the plane
from the runway if the pilot lowers the nose at an angle of depression of 12o to meet the runway?
4) A straight water slide makes a 40° angle with the surface of the water. If the slide is 11.5 meters high,
how long is it?
5) How do you think the length of a shadow of a 30 foot tree will change over the course of a sunny day?
Answer the following questions to determine if your hypothesis is correct.
A) Find the length of the shadow when the angle of elevation of the sun is 250 up from the horizon.
B) Find the length of the shadow when the angle of elevation of the sun is 700 up from the horizon.
C) Find the angle of elevation of the sun if the shadow is 23 feet long.
Algebra & Analytic Geometry
Trigonometry – Word Problem Applications
Name & Date
Finding Angle Measures Using Trigonometric Function Inverses
6) If you are given the sine, cosine or tangent of an angle, use their inverse functions: sin-1, cos-1, or tan-1 to
find the corresponding angle. Use a calculator to find  to the nearest tenth of a degree.
A)
B)
C)
4
3
8
15
θ
12
θ
5
3
θ
7) A garage is 8 feet above the level street. The driveway from the street to the garage is 45 feet long. Find
the driveway’s angle of incline.
8) What is the measure of the angle made by a 200 foot supporting cable with a 150 foot tall cell phone tower?
9) An observer on a sea cliff with a height of 12m spots a shark-fin through a pair of binoculars at an angle of
depression of 5.7.
A) To the nearest meter, how far is the shark from the base of the cliff?
B) A few minutes later, the observer spots the same shark at an angle of depression of 7.6. To the
nearest meter, how much closer has the shark moved to the base of the cliff?
10) A tree 10 meters high casts a 17.3 meter shadow. Find the angle of elevation of the sun.
11) A great white shark swims 22 feet below the sea level. If the shark is 67.7 feet from the sailboat, what is
the angle of depression of the boat to the shark?
12) A plane flying at 33,000 feet is 130 miles from the airport when it begins to descend. If the angle of
descent is constant, find this angle. (1 mile = 5280 feet)
Algebra & Analytic Geometry
Trigonometry – Word Problem Applications
13)
Name & Date
14)
x
11
20
42°
11
θ
15) A kite with a string 150 feet long makes an angle of 40 with the ground. Assuming the string is straight,
how high is the kite?
16)
17)
9
4
x
θ
68°
18
18) A plane is flying at an altitude of 36,000 feet. From the pilot, the angle of depression to the airport tower
is 32. How far is the tower from a point directly beneath the plane?
19)
20)
θ
θ
x
y
3
12
x
35°
11
3
21) An airplane takes off 200 yards in front of a 60 foot building. At what angle of elevation must the plane
take off in order to avoid crashing into the building? Assume that the airplane flies in a straight line and the
angle of elevation remains constant until the airplane flies over the building.
22)
23)
θ
9
y
40
12
x
x
θ
41
5
24) A person stands at the window of a building so that his eyes are 12.6 meters above the level ground. An
object is on the ground 58.5 meters away from the building on a line directly beneath the person. Compute the
angle of depression of the person’s line of sight to the object on the ground.