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Name_______________
Right Triangle Trigonometry Applications Date_____________
1. A 300-foot high tower stands on level ground, anchored by two cables on
the west side. The end of the cable closest to the tower makes and angle
of 68˚ with the horizontal. The two cables are 100 feet apart. How long
are the cables?
C1 – 323.56
C2 – 372.74
2. Airplane is flying at an elevation of 5150 feet, directly above a straight
highway. Two motorists are driving cars on the highway on opposite sides
of the plane and the angle of depression to one car is 35  and to the
other car is 52, how far apart are the cars?
d  11,378.58
3. If both cars in problem 3 are driving on the same side of the plane and if
the angle of depression remains the same for both cars, find the
distance between the two cars.
d  3,331.34
4. A pilot measures the angles of depression to two ships to be 40 and 52.
If the pilot is flying at an elevation of 35,000 feet, find the distance
between the two ships if they are on opposite sides of the plane.
d = 69056.37
5. A water tower is located 325 feet from a building. From a window in the
building it is observed that the angle of elevation to the top of the tower
is 39 and the angle of depression to the bottom of the tower is 25.
How tall is the tower? How high is the window?
d  414.73 feet
6. When an airplane leaves the runway, its angle of climb is 18 and its speed
is 275 feet per second. Find the altitude of the plane after one minute.
d  5, 098.78 feet
7. Find the angle of depression from the top of a lighthouse 250 feet above
the water level to the water line of a ship 2 miles offshore.
Analysis
Right Triangle Trigonometry Applications
d  1.36
Page 2
8. Observers at points J and K, sight an airplane at angles of elevation of
40° and 75° respectively. If the plane is flying at an altitude of 32,000
feet, how far is the plane from each observer?
49,783.16 ft
33,128.84 ft
9. A man standing 210 feet away from a building notices a flagpole at the
top of the building. The angle of elevation from the man to the base of
the flagpole is 21 and the elevation to the top of the flagpole is 25.
How tall is the flagpole?
17.31 ft
10. From a point on ground level, you measure the angle of elevation to the
top of a mountain to be 42°. Than you walk 300 feet further away and
find that the angle of elevation is now 20°. Find the height of the
mountain.
183.28 ft
11.
A surveyor stands 30 yards from the base of a building. At the top of
the building is a statue dedicated to Mr. C. The surveyor looks to the top
of the building at an angle of elevation of 35 ° and to the top of the
statue at an angle of 50°. Find the height of the statue.
44.24 ft (14.74 yds)
Analysis
Right Triangle Trigonometry Applications
Page 3
12. Two ships at points P and Q are in the same vertical plane as an airplane
located in the air at point R. When the height of the plane is 3500 feet,
the angle of depression to point P is 48° and that to Q is 25°. Find the
distance between the two ships if…
10,657.19
4354.36
a) the two ships are on opposite sides of the plane
b) the two ships are on the same side of the plane.