Download Right Triangle Trig Word Problems

Right Triangle Trig Word Problems
Name______________
1. A flagpole casts a 42-foot shadow. If the angle of elevation of the sun is 57.4, what is the height of the
flagpole?
2. A 37-foot tree casts a 27-foot shadow. What is the angle of elevation of the sun?
3. An airplane is flying at 4000 feet above the ground. If the angle of depression from the airplane to the
beginning of the runway is 5.4, what is the horizontal distance to the nearest tenth of a mile of the airplane to
the beginning of the runway?
4. A group of Boy Scouts on a straight trail headed N30.6 E found the trail led through a briar patch. They
chose to walk 156 meters due east along the south edge of the briar patch, then due north along the east edge
of the patch back to the trail. How much farther did they walk to avoid walking through the briar patch?
5. In the San Gabriel Mountains in California, lookout station Running Deer is 18 kilometers due west of station
Lazy Bear. The bearing from Running Deer to a fire directly south of Lazy Bear is S38.4E. To the nearest
tenth of a kilometer, how far is the fire from Running Deer? From Lazy Bear?
6. A ship is 15 miles due west of lighthouse A on the island of Hawaii. If lighthouse B is 6.2 miles due south of
lighthouse A, what is the bearing to the nearest tenth of a degree of the ship from lighthouse B? To the nearest
tenth of a mile, how far is the ship from lighthouse B?
7. A balloon flying at 3000 feet above the ocean measures the angles of depression of each end of an island
directly in front of the balloon to be 75.8 and 15.6. What is the length of the island to the nearest tenth of a
mile?
8. To measure the height of a tree, a surveyor walked a short distance from the tree and found the angle of
elevation to be 43.9, then walked 20 feet farther and measured the angle of elevation to be 37.6. Find the
height of the tree.
9. An observer standing on a cliff 320 feet above the ocean measured angles of depression of the near and far
sides of an island to be 16.5 and 10.5 respectively. How long is the island to the nearest foot?
10. Two observers, 7220 feet apart, observe a balloonist flying overhead between them. Their measures of the
angles of elevation at 3:30pm are 35.6 and 58.2 respectively. What is the height of the balloonist above the
ground?
11. An observer stands 120 feet away from a church and measures the angles of elevation of the top and bottom of
the steeple to be 24.4 and 18.2 respectively. What is the height of the steeple to the nearest foot?
12. A 40-foot flagpole stands on the top of a hill. To measure the height of the hill, a surveyor standing at the base
of the hill finds the measure of the angles of elevation of the top and bottom of the flagpole to be 49.7 and
39.3 respectively. Find the height of the hill to the nearest foot.
13. A blimp is flying parallel to a road and is 2460 feet directly above it. The angles of depression of two parked
cars on the road are 34.9 and 26.5. TO the nearest foot, how far apart are the parked cars? (Note: The blimp
is above a line between the parked cars.)
14. A fly, buzzing about the room, calculates the angle of depression of the base of an 8-foot wall is 33.7 and the
angle of elevation of the top of the wall is 12.5. Find to the nearest foot the horizontal distance the fly is from
the wall.