All Sorts of Trig Word Problems
1. John wants to measure the height of a tree. He walks exactly 100 ft from the base of the
tree and looks up. The angle from the ground to the top of the tree is 33o. This particular
tree grows at an angle of 83o with respect to the ground. How tall is the tree?
2. The road from Westville to Centerville is 10 miles long, and from Centerville to Eastville is 15
miles long. The two roads meet at angle of 126o. A telephone company wants to place a
cable that connects Westville and Eastville directly.
a. How long will the cable be?
b. What angle will the cable make with the road from Eastville to Centerville?
3. A crew is given the job of measuring the height of a mountain. From a point on level
ground, they measure an angle of elevation to the top to be 21o. They move 507 m closer
and the angle is now 35o to the top. How high is the mountain?
4. A building is of unknown height. AT a distance of 100 ft away from the building, an
observer notices that the angle of elevation to the top of the building is 41o and that the
angle of elevation to a poster on the side of the building is 21o. How far is the poster from
the roof of the building?
5. Two people are walking toward each other on a path through the park. The path runs east
and west. A hot air balloon is directly above the path between them. One of the walkers, a
female, sees the balloon when looking east at an angle of elevation of 46o. The other
walker, a male, sees the balloon looking west at an angle of elevation of 72o. If the walkers
are 55 yards apart, how far is the balloon from the male?
6. Two airplanes leave an airport, and the angle between their flight paths is 40o. An hour
later, one plane has traveled 300 miles while the other has traveled 200 miles. How far
apart are the planes at this time?
7. After a hurricane, a small tree was leaning. To keep it from falling, we nailed a 6 foot strap
into the ground 4 feet away from the base of the tree. If we attached the strap to the tree
3.5 ft up the tree, how far off the vertical was the tree leaning?
8. You observe two hot air balloons at equal altitudes. The first balloon is 12 miles from the
airport and the second is 17 miles from the airport. The observed angle between them is
a. How far apart are the balloons?
b. What angle will the first balloon make with the straight line to the airport and the
straight line to the second balloon?
9. A crow is on the ground 80 m from the base of a 45 m tall tree. It then flies straight
through the air to the top of the tree. What is the angle of the crow’s flight path relative to
the ground? If the crow’s flying speed is 10 cm/s, how long will it take for it to reach the
top of the tree?
10. Two ships leave a harbor at the same time, traveling on courses that have an angle of 140
degrees between them. If the first ship travels at 26 miles/h and the second ship travels 34
miles/h, how far apart are the two ships after 3 hours?
11. A triangular parcel of land has sides of length 680 ft, 320 ft and 802 ft. What is the area of
the parcel of land? If land is valued at $2100 per acre, what is the value of the parcel of
land? (Note: 1 acre is 43560 square feet)
12. A plane descends at an angle of depression of 20o. If it travels at a speed of 550 m/s
(along the line created by the angle of depression) for 1 minute, how much altitude has it
13. A pilot approaching a 3000 m long runway finds the angles of depression of the ends of the
runway are 14o and 20o. How far is the plane from the nearer end of the runway?
14. The Taminator needs to go to the other side of the lake (we’ll call this “point B”), which is
known to be 10 km wide. After traveling 5 km/h (by boar), she realized she had bee
traveling 15o off track. At that point, she turned the boar so that she would be heading in
the right direction. How far must she go to get to point B?
15. The Taminator is sailing in her boat, when she catches sight of a lighthouse. At a distance
of 230 m from the lighthouse, she determines that angle of elevation from her boat to the
bottom of the lighthouse to be 12o, and that the angle of elevation to the top of the
lighthouse is a further 29 o on top of this. How tall is the lighthouse?
1. 60.60 2.a) 22.39 b) 21.18 3. 430.78 4. 48.54 5. 44.8
6. 195.13 7. 16.07 8.a) 17.13 b) 69.05 9.a) 29.36 b) 917.87
10. 169.34 11. 5159.69 12. 11286.67 13. 6943.24 14. 5.33 15. 151.05