Study Guide and Review - Chapter 12 Determine whether each triangle has no solution, one solution, or two solutions. Then solve each triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.
30. C = 118°, c = 10, a = 4
SOLUTION: Because is obtuse and c > a, one solution exists.
Use the Law of Sines to find
.
Use the Law of Sines to find b.
ANSWER: one solution; A ≈ 21°, B ≈ 41°, b ≈ 7.4
31. A = 25°, a = 15, c = 18
SOLUTION: Since is acute and a < c, find h and compare it to a.
Since 7.6 < 15 < 18 or h < a < c, there is two solutions. So, there are two triangles to be solved.
eSolutions Manual - Powered by Cognero
Page 1
ANSWER: one solution; A ≈ 21°, B ≈ 41°, b ≈ 7.4 Study Guide and Review - Chapter 12 31. A = 25°, a = 15, c = 18
SOLUTION: Since is acute and a < c, find h and compare it to a.
Since 7.6 < 15 < 18 or h < a < c, there is two solutions. So, there are two triangles to be solved.
ANSWER: two solutions; First solution: C = 30°, B = 125°, b = 29.1; second solution: C = 150°, B = 5°, b = 3.1
32. A = 70°, a = 5, c = 16
SOLUTION: Since is acute and a < c, find h and compare it to a.
eSolutions Manual - Powered Since 5 < 15 or a < by h,Cognero there is
no solution.
Page 2
ANSWER: two solutions; solution: C = 30°, B = 125°, b = 29.1; second solution: C = 150°, B = 5°, b = 3.1 Study Guide and First Review - Chapter 12
32. A = 70°, a = 5, c = 16
SOLUTION: Since is acute and a < c, find h and compare it to a.
Since 5 < 15 or a < h, there is no solution.
ANSWER: no solution
33. BOAT Kira and Mallory are standing on opposite sides of a river. How far is Kira from the boat? Round to the nearest tenth if necessary.
SOLUTION: Measure of angle at boat is 180º – (85º + 30º) or 65º.
Let x be the distance between Kira and the boat.
Use the Law of Sines to find x.
ANSWER: 98.9 ft
eSolutions Manual - Powered by Cognero
Page 3
