Applications of Right Triangles
1. From a point 153 ft from the base of a flagpole, the angle of
elevation of the top is 23 °. Find the height of the flagpole.
2. From an observation balloon which is 250 ft high, the angle of
depression to an object on the ground is 8°50'. How far is the object
from a point on the ground directly under the balloon?
pilot flies on a level course at an altitude of 2000ft. He
rves that an object on the ground straight ahead has an angle of
depression of 10° and that 15 sec later the same object has an angle
of depression of 21°. What is the plane's speed in miles per hour?
4. An airplane, flying at a constant altitude, is observed flying directly
toward us and at a given instant we observe the angle of elevation of
the plane to be 8 °40'. Fifteen seconds later the plane is directly
overhead and we estimate its speed to be 300 mph. How high is the
plane flying (in feet) ?
5. Two ships start from the same place at the same time and one sails
for 3 hr on a course of N 22 °W at 12 knots (nautical miles per hour),
while the other sails for 3 hr on a course of S 68° W at 15 knots.
Determine the distance between the ships and the bearing from the
first to the second at the end of the 3 hours.
6. A ship sails for 5 hr on a course of N 3°E at 15 knots and then sails
for 7 hr on a course of N 87° W at 14 knots. At the end of the 12 hr,
how far is the ship from its starting place and what is the bearing of
the ship from its starting place?
7. An aircraft carrier is sailing on a course of S 27° W with a speed of
30 knots. At the same time and from the same place, a plane takes
off and flies on a course of S 63 ° E at a speed of 250 knots. What is
the distance and bearing from the plane to the carrier at the end of 5
hours?
in airplane pilot observes that two buoys in the water under him
angles of depression of 17° and 24° respectively. The buoys are
known to be 2 mi apart and a point directly under the plane is on the
line joining the two buoys and between them, how high is the plane?
9. From the top of a lighthouse, 150 ft above sea level, the angle of
depression to a buoy is 13 °24' and, looking in the same direction, to a
point on shore is 63 ° 17'. How far from shore is the buoy?
10. An observer on the eleventh floor of Building A determines that
the angle of depression to the foot of Building B across the street is
59 ° and that the angle of elevation to the top of Building Bis 79°. If
the street is 70 ft wide, find the height of Building B.
11. The driver of a car looking left observes that a forest ranger's
lookout tower is in a direction which makes an angle of 15° with the
highway. After driving 10 mi he notes that the direction to the
lookout tower makes an angle of 28° with the highway. Assuming that
the road is straight, how far is the lookout tower from the highway?
12. A motorist on a level highway observes that the angle of elevation
to the top of a distant mountain is 5° and after driving 8 mi directly
toward the mountain she observes that the angle of elevation to the
top of the mountain is 7°. How high above the road is the top of the
mountain?
13. An observer on the ground is 200 ft from a building that has a
flagpole on top of it. He observes that the angle of elevation to the
top of the building is 24° 10' and that the angle of elevation to the top
of the flagpole is 28 °50'. What is the height of the flagpole?
14. While flying over a small lake, a pilot, at an altitude of 1000 ft,
observes that the angle of depression to a point on the East side of
the lake is 12 °30' and that the angle of depression to a point on the
West side of the lake is 14°. Assuming that the point directly under
the plane is in the lake on the line joining the two points on the shore
of the lake, how far is it across the lake from East to West?
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