MATH 111 – Week 5 – Oblique Triangles and the Law of Sines and Cosines Exam

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MATH 111 – Week 5 – Oblique Triangles and the Law of Sines and Cosines Exam

A buoy on the ocean is rising and falling in a wave that represents the sinusoidal function, h(x) = 2cos(0.2x) + 26 in which h is height in feet above the ocean floor. What is the amplitude of the wave?

0.2 ft
2 ft
4 ft
13 ft
26 ft

A buoy on the ocean is rising and falling in a wave that represents the sinusoidal function, h(x) = 2cos(0.2x) + 26 in which h is height in feet above the ocean floor. If there were no waves, how deep would the water be where the buoy is floating?

2 ft
15 ft
24 ft
26 ft
28 ft

A buoy on the ocean is rising and falling in a wave that represents the sinusoidal function, h(x) = 2cos(0.2x) + 26 in which h is height in feet above the ocean floor. What is the maximum height of the buoy above the ocean floor?

2 ft
15 ft
24 ft
26 ft
28 ft

A buoy on the ocean is rising and falling in a wave that represents the sinusoidal function, h(x) = 2cos(0.2x) + 26 in which h is height in feet above the ocean floor. What is the wavelength of the waves going past the buoy?

14 ft
26 ft
31 ft
48 ft
52 ft

A team of astronauts is training for being weightless in space by riding in an airplane which is flying in a sinusoidal curve – the airplane flies high and then turns steeply down to mimic free fall, and hence weightlessness for the astronauts, before flying back to the top of the curve. The path of the airplane can be modeled using the function h(x) = 10000cos(0.0001x) + 20000 in which h indicates the height in feet. What is the amplitude of the wave?

0.0001
100
10,000
20,000
40,000

5,000 ft
10,000 ft
15,000 ft
20,000 ft
30,00 ft

The path of the airplane the astronauts are flying in can be modeled using the function h(x) = 10000cos(0.0001x) + 20000 in which h indicates the height in feet. What is the approximate period of the wave?

11,500 ft
23,000 ft
44,200 ft
54,600 ft
62,800 ft

The path of the airplane the astronauts are flying in can be modeled using the function h(x) = 10000cos(0.0001x) + 20000 in which h indicates the height in feet. For roughly how far will the astronauts free fall each time the airplane completes a full cycle?

10,000 ft
18,000 ft
20,000 ft
28,000 ft
32,000 ft

The path of the airplane the astronauts are flying in can be modeled using the function h(x) = 10000cos(0.0001x) + 20000 in which h indicates the height in feet. If the airplane averages 200 miles per hour in the forward direction (so not the speed of the plane, but the speed of the plane in the horizontal direction), roughly how many cycles can the airplane complete in an hour? Note that there are 5,280 ft in a mile.

Find the length of side a.

3.1
3.8
4.3
4.9
5.6

Find the measure of angle C.

75˚
82˚
88˚
90˚
94˚

Find the length of side c.

5.6
6
6.3
6.7
7.4

Find the length of side a.

7.8
8.3
9.2
9.8
10.6

Find the measure of angle B.

73˚
76˚
80˚
84˚
88˚

Find the measure of angle C.

42˚
46˚
50˚
54˚
57˚

If the lengths of the sides of a triangle are a, b, and c, and the height of the triangle is equal to side b, which describes the triangle?

The triangle doesn’t exist.
Only one triangle, a right triangle exists.
Only one triangle, a scalene triangle exists.
Two potential triangles exist.
None of the above.

If the lengths of the sides of a triangle are a, b, and c, and side b is longer than the height but shorter than side a, which describes the triangle?

The triangle doesn’t exist.
Only one triangle, a right triangle exists.
Only one triangle, a scalene triangle exists.
Two potential triangles exist.
None of the above.

What is the area of the triangle?

13.8
18.6
27.5
35.1
42.3