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.124views
Multiple ChoiceUse the Law of Cosines to find the angle CCC, rounded to the nearest tenth.127views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 3.0 ft, b = 5.0 ft, c = 6.0 ft132views
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 2x223views
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)246views
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°)321views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.234views
Textbook QuestionIn oblique triangle ABC, C = 68°, a = 5, and b = 6. Find c to the nearest tenth.283views
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 3x205views
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 = 12161views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.249views
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°232views
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°215views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.164views
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 12262views
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 12232views
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 C140views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 41.4°, b = 2.78 yd, c = 3.92 yd176views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 9.3 cm, b = 5.7 cm, c = 8.2 cm151views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 42.9 m, b = 37.6 m, c = 62.7 m163views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 965 ft, b = 876 ft, c = 1240 ft130views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 80° 40', b = 143 cm, c = 89.6 cm128views
Textbook QuestionSolve each triangle. See Examples 2 and 3.B = 74.8°, a = 8.92 in., c = 6.43 in.166views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 112.8°, b = 6.28 m, c = 12.2 m149views
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 C225views
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?172views
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.)144views
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>206views
Textbook QuestionFind the length of the remaining side of each triangle. Do not use a calculator.<IMAGE>229views
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 = 48.2138views
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°190views
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°192views
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°199views
Textbook QuestionIn Exercises 14–19, use a sum or difference formula to find the exact value of each expression. cos(45° + 30°)302views
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 meters204views
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°243views
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 meters266views
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°)226views
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 = 10186views
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 = 8169views
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 = 3424views
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 = 50202views
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 feet264views
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 meters278views
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 yards240views
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 2214views
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 2259views
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)177views
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 2221views
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 2213views
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 13228views
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 3294views
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 2244views
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 2255views
Textbook QuestionIn Exercises 69–74, rewrite each expression as a simplified expression containing one term. cos (α + β) cos β + sin (α + β) sin β231views
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