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.108views
Multiple ChoiceUse the Law of Cosines to find the angle CCC, rounded to the nearest tenth.114views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 3.0 ft, b = 5.0 ft, c = 6.0 ft118views
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 2x186views
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)207views
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°)266views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.212views
Textbook QuestionIn oblique triangle ABC, C = 68°, a = 5, and b = 6. Find c to the nearest tenth.244views
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 3x174views
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 = 12144views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.224views
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°189views
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°180views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.145views
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 12220views
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 12197views
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 C120views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 41.4°, b = 2.78 yd, c = 3.92 yd153views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 9.3 cm, b = 5.7 cm, c = 8.2 cm126views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 42.9 m, b = 37.6 m, c = 62.7 m144views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 965 ft, b = 876 ft, c = 1240 ft120views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 80° 40', b = 143 cm, c = 89.6 cm115views
Textbook QuestionSolve each triangle. See Examples 2 and 3.B = 74.8°, a = 8.92 in., c = 6.43 in.141views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 112.8°, b = 6.28 m, c = 12.2 m129views
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 C194views
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?151views
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.)123views
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>183views
Textbook QuestionFind the length of the remaining side of each triangle. Do not use a calculator.<IMAGE>184views
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 = 48.2119views
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°167views
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°168views
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°180views
Textbook QuestionIn Exercises 14–19, use a sum or difference formula to find the exact value of each expression. cos(45° + 30°)254views
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 meters181views
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°208views
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 meters233views
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°)188views
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 = 10158views
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 = 8150views
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 = 3376views
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 = 50188views
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 feet226views
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 meters241views
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 yards213views
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 2182views
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 2221views
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)156views
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 2183views
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 2181views
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 13188views
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 3259views
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 2198views
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 2209views
Textbook QuestionIn Exercises 69–74, rewrite each expression as a simplified expression containing one term. cos (α + β) cos β + sin (α + β) sin β192views
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