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Problem 7.55
Find the angle between each pair of vectors. Round to two decimal places as necessary.
〈2, 1〉, 〈-3, 1〉
Problem 7.55
Find the area of each triangle ABC.
A = 56.80°, b = 32.67 in., c = 52.89 in.
Problem 7.56
A pilot is flying at 168 mph. She wants her flight path to be on a bearing of 57° 40′. A wind is blowing from the south at 27.1 mph. Find the bearing she should fly, and find the plane's ground speed.
Problem 7.58
Find the angle between each pair of vectors. Round to two decimal places as necessary.
〈4, 0〉, 〈2, 2〉
Problem 7.58
Find the area of each triangle ABC.
A = 59.80°, b = 15.00 cm, C = 53.10°
Problem 7.58
A plane is headed due south with an airspeed of 192 mph. A wind from a direction of 78.0° is blowing at 23.0 mph. Find the ground speed and resulting bearing of the plane.
Problem 7.59
A painter is going to apply paint to a triangular metal plate on a new building. Two sides measure 16.1 m and 15.2 m, and the angle between the sides is 125°. What is the area of the surface to be painted?
Problem 7.60
A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are 52.1 m and 21.3 m, and the angle between them is 42.2°. What is the area of the triangular lot?
Problem 7.61
Find the angle between each pair of vectors. Round to two decimal places as necessary.
〈1, 6〉, 〈-1, 7〉
Problem 7.63
Find the angle between each pair of vectors. Round to two decimal places as necessary.
3i + 4j, j
Problem 7.63
Find the exact area of each triangle using the formula 𝓐 = ½ bh, and then verify that Heron's formula gives the same result.
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Problem 7.65
Find the angle between each pair of vectors. Round to two decimal places as necessary.
2i + 2j, -5i - 5j
Problem 7.67
Let u = 〈-2, 1〉, v = 〈3, 4〉, and w = 〈-5, 12〉. Evaluate each expression.
(3u) • v
Problem 7.69
Let u = 〈-2, 1〉, v = 〈3, 4〉, and w = 〈-5, 12〉. Evaluate each expression.
u • v - u • w
Problem 7.69
Find the area of each triangle ABC.
a = 76.3 ft, b = 109 ft, c = 98.8 ft
Problem 7.7
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.
<IMAGE>
2c
Problem 7.7
Determine the number of triangles ABC possible with the given parts.
a = 31, b = 26, B = 48°
Problem 7.72
Determine whether each pair of vectors is orthogonal.
〈1, 1〉, 〈1, -1〉
Problem 7.75
Determine whether each pair of vectors is orthogonal.
√5i - 2j, -5i + 2 √5j
Problem 7.78
Determine whether each pair of vectors is orthogonal.
i + 3√2j, 6i - √2j
Problem 7.9
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.
〈5, 7〉
Problem 7.9
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.
<IMAGE>
a + b
Problem 7.9
Determine the number of triangles ABC possible with the given parts.
c = 50, b = 61, C = 58°
Problem 7.9
Find the length of the remaining side of each triangle. Do not use a calculator.
<IMAGE>
Problem 10
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.
〈-4, -7〉
Problem 12
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary. See Example 1.
〈-7, 24〉
Problem 14
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary. See Example 1.
〈8√2, -8√2〉