Multiple ChoiceA surveyor wishes to find the distance across a river while standing on a small island. If she measures distances of a=30ma=30ma=30m to one shore, c=60mc=60mc=60m to the opposite shore, and an angle of B=100°B=100\degreeB=100° between the two shores, find the distance between the two shores.130views
Multiple ChoiceUse the Law of Cosines to find the angle CCC, rounded to the nearest tenth.137views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 3.0 ft, b = 5.0 ft, c = 6.0 ft145views
Textbook QuestionBe sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference. sin 6x sin 2x236views
Textbook QuestionUse the following conditions to solve Exercises 1–4: 4 𝝅 sin α = ----- , ------- < α < 𝝅 5 2 5 𝝅 cos β = ------ , 0 < β < ------ 13 2 Find the exact value of each of the following. cos (α + β)259views
Textbook QuestionUse the formula for the cosine of the difference of two angles to solve Exercises 1–12. In Exercises 1–4, find the exact value of each expression. cos(45° - 30°)342views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.251views
Textbook QuestionIn oblique triangle ABC, C = 68°, a = 5, and b = 6. Find c to the nearest tenth.299views
Textbook QuestionBe sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference. cos 7x cos 3x216views
Textbook QuestionIn Exercises 1–12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state 'no triangle.' If two triangles exist, solve each triangle. B = 66°, a = 17, c = 12172views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.262views
Textbook QuestionIn Exercises 5–8, each expression is the right side of the formula for cos (α - β) with particular values for α and β. c. Find the exact value of the expression. cos 50° cos 20° + sin 50° sin 20°253views
Textbook QuestionIn Exercises 5–8, each expression is the right side of the formula for cos (α - β) with particular values for α and β. b. Write the expression as the cosine of an angle. cos 50° cos 20° + sin 50° sin 20°231views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.180views
Textbook QuestionIn Exercises 5–8, each expression is the right side of the formula for cos (α - β) with particular values for α and β. c. Find the exact value of the expression. 5π π 5π π cos ------- cos -------- + sin -------- sin ------- 12 12 12 12277views
Textbook QuestionIn Exercises 5–8, each expression is the right side of the formula for cos (α - β) with particular values for α and β. b. Write the expression as the cosine of an angle. 5π π 5π π cos ------- cos -------- + sin -------- sin ------- 12 12 12 12245views
Textbook QuestionCONCEPT 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 C150views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 41.4°, b = 2.78 yd, c = 3.92 yd188views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 9.3 cm, b = 5.7 cm, c = 8.2 cm166views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 42.9 m, b = 37.6 m, c = 62.7 m175views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 965 ft, b = 876 ft, c = 1240 ft144views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 80° 40', b = 143 cm, c = 89.6 cm139views
Textbook QuestionSolve each triangle. See Examples 2 and 3.B = 74.8°, a = 8.92 in., c = 6.43 in.180views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 112.8°, b = 6.28 m, c = 12.2 m167views
Textbook QuestionCONCEPT 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 C238views
Textbook QuestionA 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?188views
Textbook QuestionFind 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.)156views
Textbook QuestionFind the exact area of each triangle using the formula 𝓐 = ½ bh, and then verify that Heron's formula gives the same result.<IMAGE>215views
Textbook QuestionFind the length of the remaining side of each triangle. Do not use a calculator.<IMAGE>240views
Textbook QuestionIn Exercises 1–12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state 'no triangle.' If two triangles exist, solve each triangle. A = 162°, b = 11.2, c = 48.2154views
Textbook QuestionIn Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 5, b = 7, C = 42°204views
Textbook QuestionIn Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. b = 5, c = 3, A = 102°205views
Textbook QuestionIn Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 6, c = 5, B = 50°218views
Textbook QuestionIn Exercises 14–19, use a sum or difference formula to find the exact value of each expression. cos(45° + 30°)311views
Textbook QuestionIn Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit. a = 2 meters, b = 4 meters, c = 5 meters213views
Textbook QuestionIn Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 5, c = 2, B = 90°258views
Textbook QuestionIn Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit. a = 2 meters, b = 2 meters, c = 2 meters285views
Textbook QuestionUse one or more of the six sum and difference identities to solve Exercises 13–54. In Exercises 13–24, find the exact value of each expression. cos(135° + 30°)238views
Textbook QuestionIn Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 5, b = 7, c = 10202views
Textbook QuestionIn Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 3, b = 9, c = 8181views
Textbook QuestionIn Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 3, b = 3, c = 3441views
Textbook QuestionIn Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 63, b = 22, c = 50216views
Textbook QuestionIn Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit. a = 4 feet, b = 4 feet, c = 2 feet281views
Textbook QuestionIn Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit. a = 14 meters, b = 12 meters, c = 4 meters296views
Textbook QuestionIn Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit. a = 11 yards, b = 9 yards, c = 7 yards257views
Textbook QuestionIn Exercises 35–38, find the exact value of the following under the given conditions: β e. cos ------- 2 3 𝝅 12 𝝅 sin α = ------- , 0 < α < -------- , and sin β = --------- , --------- < β < 𝝅. 5 2 13 2227views
Textbook QuestionIn Exercises 35–38, find the exact value of the following under the given conditions: b. cos(α﹣β) 3 𝝅 12 𝝅 sin α = ------- , 0 < α < -------- , and sin β = --------- , --------- < β < 𝝅. 5 2 13 2270views
Textbook QuestionIn Exercises 35–36, the three given points are the vertices of a triangle. Solve each triangle, rounding lengths of sides to the nearest tenth and angle measures to the nearest degree. A(0, 0), B(-3, 4), C(3, -1)191views
Textbook QuestionIn Exercises 35–38, find the exact value of the following under the given conditions: β e. cos ------- 2 1 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2235views
Textbook QuestionIn Exercises 35–38, find the exact value of the following under the given conditions: b. cos(α﹣β) 1 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2224views
Textbook QuestionIn Exercises 57–64, find the exact value of the following under the given conditions: a. cos (α + β) 3 5 sin α = ------ , α lies in quadrant I, and sin β = ------- , β lies in quadrant II. 5 13238views
Textbook QuestionIn Exercises 57–64, find the exact value of the following under the given conditions: a. cos (α + β) 3 1 tan α = ﹣ ------ , α lies in quadrant II, and cos β = ------- , β lies in quadrant I. 4 3306views
Textbook QuestionIn Exercises 57–64, find the exact value of the following under the given conditions: a. cos (α + β) 8 1 cos α = ------ , α lies in quadrant IV, and sin β = ﹣------- , β lies in quadrant III. 17 2258views
Textbook QuestionIn Exercises 57–64, find the exact value of the following under the given conditions: a. cos (α + β) 3 3𝝅 1 3𝝅 tan α = ------ , 𝝅 < α < -------- , and cos β = ------- , ---------- < β < 2𝝅. 4 2 4 2270views
Textbook QuestionIn Exercises 69–74, rewrite each expression as a simplified expression containing one term. cos (α + β) cos β + sin (α + β) sin β246views
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