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Problem 7.4
Use the law of sines to find the indicated part of each triangle ABC.
Find b if a = 165 m, A = 100.2°, B = 25.0°
Problem 7.4
CONCEPT PREVIEW Assume a triangle ABC has standard labeling.
a. Determine whether SAA, ASA, SSA, SAS, or SSS is given.
b. Determine whether the law of sines or the law of cosines should be used to begin solving the triangle.
a, B, and C
Problem 7.41
A force of 18.0 lb is required to hold a 60.0-lb stump grinder on an incline. What angle does the incline make with the horizontal?
Problem 7.41a
Given vectors u and v, find: 2u.
u = 2i, v = i + j
Problem 7.41b
Given vectors u and v, find: 2u + 3v.
u = 2i, v = i + j
Problem 7.41c
Given vectors u and v, find: v - 3u.
u = 2i, v = i + j
Problem 7.42
A force of 30.0 lb is required to hold an 80.0-lb pressure washer on an incline. What angle does the incline make with the horizontal?
Problem 7.43
Two people are carrying a box. One person exerts a force of 150 lb at an angle of 62.4° with the horizontal. The other person exerts a force of 114 lb at an angle of 54.9°. Find the weight of the box.
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Problem 7.43a
Given vectors u and v, find: 2u.
u = 〈-1, 2〉, v = 〈3, 0〉
Problem 7.43b
Given vectors u and v, find: 2u + 3v.
u = 〈-1, 2〉, v = 〈3, 0〉
Problem 7.43c
Given vectors u and v, find: v - 3u.
u = 〈-1, 2〉, v = 〈3, 0〉
Problem 7.44
A crate is supported by two ropes. One rope makes an angle of 46° 20′ with the horizontal and has a tension of 89.6 lb on it. The other rope is horizontal. Find the weight of the crate and the tension in the horizontal rope.
Problem 7.45
A ship leaves port on a bearing of 34.0° and travels 10.4 mi. The ship then turns due east and travels 4.6 mi. How far is the ship from port, and what is its bearing from port?
Problem 7.46
Write each vector in the form a i + b j.
〈6, -3〉
Problem 7.46
A luxury liner leaves port on a bearing of 110.0° and travels 8.8 mi. It then turns due west and travels 2.4 mi. How far is the liner from port, and what is its bearing from port?
Problem 7.47
Write each vector in the form a i + b j.
〈2, 0〉
Problem 7.47
Starting at point A, a ship sails 18.5 km on a bearing of 189°, then turns and sails 47.8 km on a bearing of 317°. Find the distance of the ship from point A.
Problem 7.48
Find the area of each triangle using the formula 𝓐 = ½ bh, and then verify that the formula 𝓐 = ½ ab sin C gives the same result.
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Problem 7.48
Starting at point X, a ship sails 15.5 km on a bearing of 200°, then turns and sails 2.4 km on a bearing of 320°. Find the distance of the ship from point X.
Problem 7.48
One boat pulls a barge with a force of 100 newtons. Another boat pulls the barge at an angle of 45° to the first force, with a force of 200 newtons. Find the resultant force acting on the barge, to the nearest unit, and the angle between the resultant and the first boat, to the nearest tenth.
Problem 7.49
Solve each problem. See Examples 5 and 6.
Distance and Direction of a Motorboat A motorboat sets out in the direction N 80° 00′ E. The speed of the boat in still water is 20.0 mph. If the current is flowing directly south, and the actual direction of the motorboat is due east, find the speed of the current and the actual speed of the motorboat.
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Problem 7.49
A plane has an airspeed of 520 mph. The pilot wishes to fly on a bearing of 310°. A wind of 37 mph is blowing from a bearing of 212°. In what direction should the pilot fly, and what will be her ground speed?
Problem 7.5
CONCEPT PREVIEW Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.
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-b
Problem 7.5
Determine the number of triangles ABC possible with the given parts.
a = 50, b = 26, A = 95°
Problem 7.51
Find the area of each triangle ABC.
A = 42.5°, b = 13.6 m, c = 10.1 m
Problem 7.51
Solve each problem. See Examples 5 and 6.
Bearing and Ground Speed of a Plane An airline route from San Francisco to Honolulu is on a bearing of 233.0°. A jet flying at 450 mph on that bearing encounters a wind blowing at 39.0 mph from a direction of 114.0°. Find the resulting bearing and ground speed of the plane.
Problem 7.51
Find the force required to keep a 75-lb sled from sliding down an incline that makes an angle of 27° with the horizontal. (Assume there is no friction.)
Problem 7.53
Find the dot product for each pair of vectors.
4i, 5i - 9j
Problem 7.53
Find the area of each triangle ABC.
B = 124.5°, a = 30.4 cm, c = 28.4 cm
Problem 7.54
A plane flies 650 mph on a bearing of 175.3°. A 25-mph wind, from a direction of 266.6°, blows against the plane. Find the resulting bearing of the plane.