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Problem 6.31
Apply the law of sines to the following: a = √5, c = 2√5, A = 30°. What is the value of sin C? What is the measure of C? Based on its angle measures, what kind of triangle is triangle ABC?
Problem 6.33
Without using the law of sines, explain why no triangle ABC can exist that satisfies A = 103° 20', a = 14.6 ft, b = 20.4 ft.
Problem 6.34
Apply the law of sines to the following:
A = 104°, a = 26.8, b = 31.3.
What happens when we try to find the measure of angle B using a calculator?
Problem 6.40
Use the law of sines to prove that each statement is true for any triangle ABC, with corresponding sides a, b, and c.
(a - b)/(a + b) = (sin A - sin B)/(sin A + sin B)
Problem 7.1
Fill in the blank(s) to correctly complete each sentence.
A triangle that is not a right triangle is a(n) _________ triangle.
Problem 7.10
Consider each case and determine whether there is sufficient information to solve the triangle using the law of sines.
Three sides are known.
Problem 7.1
Which one of the following sets of data does not determine a unique triangle?
a. A = 50°, b = 21, a = 19
b. A = 45°, b = 10, a = 12
c. A = 130°, b = 4, a = 7
d. A = 30°, b = 8, a = 4
Problem 7.1
Use the law of sines to find the indicated part of each triangle ABC.
Find b if C = 74.2°, c = 96.3 m, B = 39.5
Problem 7.1
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 7.11
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.
〈15, -8〉
Problem 7.11
Find each angle B. Do not use a calculator.
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Problem 7.12
Find the length of each side labeled a. Do not use a calculator.
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Problem 7.13
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.
〈-4, 4√3〉
Problem 7.13
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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a + (b + c)
Problem 7.13
Find the unknown angles in triangle ABC for each triangle that exists.
A = 29.7°, b = 41.5 ft, a = 27.2 ft
Problem 7.13
Solve each triangle. Approximate values to the nearest tenth.
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Problem 7.14
Solve each triangle ABC.
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Problem 7.15
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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c + d
Problem 7.15
Find the unknown angles in triangle ABC for each triangle that exists.
C = 41° 20', b = 25.9 m, c = 38.4 m
Problem 7.15
Solve each triangle. Approximate values to the nearest tenth.
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Problem 7.16
Vector v has the given direction angle and magnitude. Find the horizontal and vertical components.
θ = 50°, |v| = 26
Problem 7.16
Solve each triangle ABC.
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Problem 7.17
Solve each triangle ABC.
A = 68.41°, B = 54.23°, a = 12.75 ft
Problem 7.17
Find the unknown angles in triangle ABC for each triangle that exists.
B = 74.3°, a = 859 m, b = 783 m
Problem 7.18
Vector v has the given direction angle and magnitude. Find the horizontal and vertical components.
θ = 27° 30' |v| = 15.4
Problem 7.18
Solve each triangle. Approximate values to the nearest tenth.
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Problem 7.19
For each pair of vectors u and v with angle θ between them, sketch the resultant.
|u| = 12, |v| = 20, θ = 27°
Problem 7.19
Find the unknown angles in triangle ABC for each triangle that exists.
A = 142.13°, b = 5.432 ft, a = 7.297 ft
Problem 7.19
Solve each triangle. See Examples 2 and 3.
A = 41.4°, b = 2.78 yd, c = 3.92 yd
Problem 7.20
Solve each triangle ABC.
B = 38° 40', a = 19.7 cm, C = 91° 40'