Sine, Cosine, and Tangent - Word Problems #2 (Grades 11-12)

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Sine, Cosine, and Tangent - Word Problems #2

1. 
The elevation of the sun is 56°. What is the length of the shadow of a tree that is 8.7 m tall? Round the answer to the nearest tenth of a meter.
  1. 0.2 m
  2. 5.9 m
  3. 10.5 m
  4. 15.6 m
2. 
Harry is building a ramp with wooden boards. If the boards are 18 ft, and the ramp will rise 6 ft, what is the angle of elevation of the ramp? Round the answer to the nearest tenth of a degree.
  1. 18.4°
  2. 19.5°
  3. 70.5°
  4. 71.6°
3. 
A slide on a playground forms a right triangle. If the angle of elevation of the slide is 51° and it is 2.6 m long, how high is the slide? Round the answer to two decimal places.
  1. 1.64 m
  2. 2.02 m
  3. 3.35 m
  4. 4.13 m
4. 
A large apartment building was recently built in a coastal city. The building was constructed away from the coastline and there are other buildings between it and the ocean, but some of the upper floors have a view of the ocean. People living above 80 m high in the apartment building can see the ocean and the beach. If the angle of elevation from the edge of the ocean to this point on the building is 26°, how far away from the ocean is the building? Round the answer to the nearest meter.
  1. 39 m
  2. 89 m
  3. 164 m
  4. 182 m
5. 
A helicopter just took off from a landing pad. It travels straight up in the air for 35 m, and then travels forward, parallel to the ground for 85 m. If a person is standing where the helicopter took off from, what is the angle of elevation from that person to where the helicopter currently is? Round the answer to the nearest tenth of a degree.
  1. 22.4°
  2. 24.3°
  3. 65.7°
  4. 67.6°
6. 
Mark is about to go on a zipline for the first time. The zipline is simply a wire, attached high up in a tree at one end and to the ground at the other. Mark will climb the tree, have the harness he's wearing connected to the wire of the zipline, and then slide down the wire. If the wire is 27 m long, and the angle of elevation of the wire is 33°, how high up in the tree is the other end? Round the answer to the nearest tenth of a meter.
  1. 14.7 m
  2. 22.6 m
  3. 32.2 m
  4. 49.6 m
7. 
Casey is helping Ed to test some satellite dishes on a tower. Casey is on the ground, 47 ft away from the base of the tower. After Ed climbs to the first satellite dish on the tower, Casey points an emitter at an angle of elevation of 49° directly at the dish. After the testing is complete, Ed climbs higher on the tower to the second satellite dish. Casey points the emitter at an angle of elevation of 68° directly at the higher dish. What is the distance between the first satellite dish and second one, rounded to one decimal place?
  1. 21.9 ft
  2. 37.9 ft
  3. 62.3 ft
  4. 116.3 ft
8. 
The main sail on a small sailboat is shaped like a right triangle. The longer leg of the triangle is attached to the mast and shorter leg is attached to the boom (a straight, horizontal piece attached to the mast). If the hypotenuse side of the sail is 9 ft long, and the angle between the mast and the hypotenuse edge of the sail is 26°, what is the area of the sail, rounded to the nearest tenth of a square foot?
  1. [math]16.0 \ "ft"^2[/math]
  2. [math]19.8 \ "ft"^2[/math]
  3. [math]31.9 \ "ft"^2[/math]
  4. [math]83.0 \ "ft"^2[/math]
9. 
Brian has a small yard in front of his house in the shape of a rectangle that is 9 ft wide by 34 ft long. However, it is not completely level. There is a flat, upper section, then a sloped section, and then a flat, lower section. The upper section spans the width of the yard, and extends for 14 ft of the length of the yard. The lower section spans the width of the yard and extends for 12 ft of the length of the yard. The sloped section accounts for the rest. Brian just planted grass seed, and has to cover the entire area of his yard with netting to keep the birds from eating the grass seed. If he needs [math]324 \ "ft"^2[/math] of netting to cover the entire yard, what is the angle of elevation of the sloped section? Round the answer to one decimal place.
  1. 64.2°
  2. 53.1°
  3. 44.7°
  4. 36.9°
10. 
An airplane has been flying in a straight line, due south, between two cities. Partway through the flight, it has to make a detour and changes direction to S36°E. After some time, but still on the detour, the plane makes another heading change to S54°W. After some more time passes, the plane changes direction again, resuming its original flight path on its original heading of due south. If the plane had to fly 530 miles on the detour, how many fewer miles would it have flown without the detour (directly south between the two cities)? Round the answer to the nearest mile.
  1. 8 miles
  2. 151 miles
  3. 372 miles
  4. Not enough information.

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