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.97views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 3.0 ft, b = 5.0 ft, c = 6.0 ft110views
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 2x167views
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)188views
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°)243views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.201views
Textbook QuestionIn oblique triangle ABC, C = 68°, a = 5, and b = 6. Find c to the nearest tenth.226views
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 3x155views
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 = 12134views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.213views
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°168views
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°164views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.133views
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 12199views
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 12177views
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 C109views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 41.4°, b = 2.78 yd, c = 3.92 yd141views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 9.3 cm, b = 5.7 cm, c = 8.2 cm117views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 42.9 m, b = 37.6 m, c = 62.7 m133views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 965 ft, b = 876 ft, c = 1240 ft111views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 80° 40', b = 143 cm, c = 89.6 cm106views
Textbook QuestionSolve each triangle. See Examples 2 and 3.B = 74.8°, a = 8.92 in., c = 6.43 in.130views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 112.8°, b = 6.28 m, c = 12.2 m120views
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 C174views
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?144views
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.)112views
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>168views
Textbook QuestionFind the length of the remaining side of each triangle. Do not use a calculator.<IMAGE>160views
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 = 48.2111views
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°155views
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°155views
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°169views
Textbook QuestionIn Exercises 14–19, use a sum or difference formula to find the exact value of each expression. cos(45° + 30°)231views
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 meters168views
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°197views
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 meters217views
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°)168views
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 = 10149views
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 = 8142views
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 = 3355views
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 = 50175views
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 feet212views
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 meters220views
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 yards201views
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 2165views
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 2202views
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)145views
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 2164views
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 2165views
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 13169views
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 3240views
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 2181views
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 2189views
Textbook QuestionIn Exercises 69–74, rewrite each expression as a simplified expression containing one term. cos (α + β) cos β + sin (α + β) sin β170views
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