Chapter 3: Laws of Sines and Cosines
Exercises: 3.2 The Law of Sines
Skills
- Use the law of sines to find a side #1-6
- Use the law of sines to find an angle #7-12
- Use the law of sines to solve an oblique triangle #13-18
- Solve problems using the law of sines #19-28
- Compute distances using the parallax #29-32
- Solve problems involving the ambiguous case #33-46
Suggested homework problems
Homework 3.2
Exercise Group
For Problems 1–6, use the law of sines to find the indicated side. Round to two decimal places.
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Exercise Group
For Problems 7–12, use the law of sines to find the indicated angle. Round to two decimal places.
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Exercise Group
For Problems 13–18, sketch the triangle and solve. Round answers to two decimal places.
13. [latex]b = 7,~ A = 23°,~ B = 42°[/latex]
14. [latex]c = 34,~ A = 53°,~ C = 26°[/latex]
15. [latex]a = 1.8,~ c = 2.1,~ C = 44°[/latex]
16. [latex]b = 8.5,~ c = 6.8,~ B = 23°[/latex]
17. [latex]c = 75,~ A = 35°,~ B = 46°[/latex]
18. [latex]a = 94,~ B = 29°,~ C = 84°[/latex]
Exercise Group
For Problems 19–26, sketch and label a triangle to illustrate the problem. Solve the problem.
19. Maryam wants to know the height of a cliff on the other side of a ravine. The angle of elevation from her edge of the ravine to the cliff top is [latex]84.6°{.}[/latex] When she moves [latex]30[/latex] feet back from the ravine, the angle of elevation is [latex]82.5°{.}[/latex] How tall is the cliff?
20. Amir wants to know the height of a tree in the median strip of a highway. The angle of elevation from the highway shoulder to the treetop is [latex]43.5°{.}[/latex] When he moves 10 feet farther away from the tree, the angle of elevation is [latex]37.2°{.}[/latex] How tall is the tree?
21. Delbert and Francine are [latex]10[/latex] kilometers apart, both observing a satellite that passes directly over their heads. At a moment when the satellite is between them, Francine measures its angle of elevation as [latex]84.6°{,}[/latex] and Delbert measures an angle of [latex]87°{.}[/latex] How far is the satellite from Delbert?
22. Megan rows her kayak due east. When she began, she spotted a lighthouse [latex]2000[/latex] meters in the distance at an angle of [latex]14°[/latex] south of east. After traveling for an hour, the lighthouse was at an angle of [latex]83°[/latex] south of east. How far did Megan travel, and what was her average speed?
23. Chad is hiking along a straight path but needs to detour around a large pond. He turns [latex]23°[/latex] from his path until clear of the pond, then walks back to his original path, intercepting it at an angle of [latex]29°[/latex] and at a distance of [latex]2[/latex] miles from where he had left the path. How far did Chad walk in each of the two segments of his detour, and how much farther did his detour require compared with a straight line through the pond?
24. Bob is flying to Monterey but must change course to avoid a storm. He flies [latex]19°[/latex] off fr