Extra Word Problems
1. On a carousel, the outer row of animals is 25 feet from the center of the carousel and the inner row of
animals is 10 feet from the center of the carousel. If the carousel makes 8 revolutions per minute, what
is the difference, in feet per minute, of an animal in the outer and inner row?
2. A child sits on a merry-go-round 2 feet from the center. It is being pushed at a rate of 1 revolution per
second. Another child sits on the same merry-go-round but 5 feet from the center. What is the linear
velocity of each child?
3. The tips of a windmill blade must travel a linear speed of 20𝜋 feet per second to generate any electricity.
If the windmill blades are 5 feet long, how many revolutions per second must the windmill make to
generate electricity?
4. A 100 foot tall tower casts a shadow of 155 feet. Find the angle of elevation of the sun to nearest tenth
of a degree.
5. A telephone pole is 70 feet tall. A 95 foot guy wire is attached from the top of the pole to the ground.
What is the angle that the wire makes with the pole?
6. When the angle of elevation of the sun is 62°, a telephone pole that is tilted at an angle of 8° away from
the sun casts a shadow 20 feet long. Determine the length of the telephone pole.
7. The angle of elevation from a point A of a tree is 32°. From a point exactly one hundred feet closer to
the tree, the angle of elevation is 44°. What is the height of the tree?
8. Two buildings are of identical height and are exactly 900 feet apart. An observer standing between the
buildings measures the angle of elevation to one building to be 52° and the other to be 62°. What is the
height of each building?
9. A boat is travelling directly north. At point A, it measures an angle of 31° west of north to a lighthouse
on the shore. At point B, it measures an angle of 55° west of south to the same lighthouse. At point B,
a lighthouse operator radios the boat to tell them they are a distance of 5350 feet away from the
lighthouse. What is the distance between point A and B?
10. Three islands are arranged in a triangle. Island A is directly west of Island B. Island C is northeast of
Island A and northwest of Island B. The distance from island A to Island B is 12 miles. The distance
from Island A to Island C is 10 miles. The distance from Island C to Island B is 14 miles. Find the
measure of each angle between each island.
11. The lengths of the diagonals of a parallelogram are 20 and 30 inches. Knowing that the diagonals of a
parallelogram bisect each other, and that these particular diagonals intersect at an angle of 35°, find the
lengths of the sides of the parallelogram.
12. The vertices of a triangle are at (3, 5), (-2, 7), and (1, -1). Find the measure of each angle of the triangle.
13. Point A is at one end of a cove. Point B is on the other side. I have measured the distance from point A
to point C, further inland from the cove to be 70 meters and the distance from point B to point C to be
110 meters. I know the angle measured from point C between points A and B to be 105°. What is the
distance across the cove from point A to point B?
14. A flagpole is attached vertically to the top of a building. An observer at ground level measures the angle
of elevation to the top of the building from 600 feet away to be 62°. He also measures the angle of
elevation from the same spot to the top of the flagpole to be 64°. How tall is the flagpole?
15. A poster is hanging on the side of a building. The angle of elevation from 300 feet away to the top of
the building is 82°. The angle of elevation from the same spot to the top of the poster is 74°. How far is
the top of the poster from the top of the building?
16. A surveyor is attempting to determine the exact length of a tunnel through a mountain. He starts at the
exit point of the tunnel and walks in a straight line for 2000 meters. He turns at an angle of 67° and
walks 3500 meters directly back to the entry point of the tunnel. How long will the tunnel be?
17. A post is supported by two wires going in opposite directions towards the ground. The angle between
the two wires is 70°. If the ends of the two wires are 15 feet apart when they hit the ground and one of
the wires makes an angle of 32° with the ground, find the length of each wire.
18. Points A and B are on opposite sides of a canyon. Point C at the bottom of the canyon is 150 yards from
Point A and 220 yards from Point B. They form an angle of 102° How far apart are points A and B?
19. A rock climber is part of the way up a sheer cliff face. Opposite him is a mountain known to be 12000
feet tall. His angle of elevation to the top of the mountain is 71° and his angle of depression to the base
of the mountain at sea level is 35°. What is the climber’s elevation?
20. A person must be within 200 miles of a radio tower to receive its broadcast signal. A person drivers 110
miles past the radio station, turns left to make an angle of 99° with the road they were driving on, and
then drives another 80 miles. Are they still within the broadcast range?
21. Two airplanes leave an airport at the same time. Plane A leaves at an angle of elevation of 35° directly
to the west. Plane B leaves at an angle of elevation of 50° directly to the east. After one hour, the
planes are still traveling at the same angles. Plane A has traveled 350 miles. Plane B has traveled 300
miles. What is the distance between the two planes?
22. A rhombus has a side length of 22 inches. Its smaller angle is 55°. Find the length of the larger
diagonal.
23. Points A and B are on one side of the river, 100 feet away from each other. Point C is on the opposite
side of the river between points A and B. The angle from Point A to Point C is 55° and the angle from
Point B to Point C is 73°. What is the distance from Point A to Point C and from Point B to Point C?
24. An isosceles triangle has a vertex angle of 40° and a base that measures 24 cm. Find the perimeter of
the triangle.
25. A house is built on a triangular piece of land. One side of the plot is 400 feet long. The adjacent side is
380 feet long. The included angle of the two sides is 75°. How many square feet is the plot? How many
feet of fencing are needed to enclose the entire plot of land?
26. A house is built on a plot of land that is an irregularly shaped quadrilateral. Point B is 700 feet due west
of Point A. Point C is 600 feet at an angle of 115° northwest of point B. Point D is 400 feet northeast of
Point A at an angle of 120°. How many square feet is the plot of land? What is the perimeter of the plot
of land?