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.116views
Multiple ChoiceUse the Law of Cosines to find the angle CCC, rounded to the nearest tenth.116views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 3.0 ft, b = 5.0 ft, c = 6.0 ft119views
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 2x193views
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)213views
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°)275views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.216views
Textbook QuestionIn oblique triangle ABC, C = 68°, a = 5, and b = 6. Find c to the nearest tenth.251views
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 3x178views
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 = 12147views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.230views
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°197views
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°186views
Textbook QuestionIn Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.148views
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 12227views
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 12203views
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 C125views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 41.4°, b = 2.78 yd, c = 3.92 yd158views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 9.3 cm, b = 5.7 cm, c = 8.2 cm130views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 42.9 m, b = 37.6 m, c = 62.7 m149views
Textbook QuestionSolve each triangle. See Examples 2 and 3.a = 965 ft, b = 876 ft, c = 1240 ft121views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 80° 40', b = 143 cm, c = 89.6 cm117views
Textbook QuestionSolve each triangle. See Examples 2 and 3.B = 74.8°, a = 8.92 in., c = 6.43 in.145views
Textbook QuestionSolve each triangle. See Examples 2 and 3.A = 112.8°, b = 6.28 m, c = 12.2 m131views
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 C202views
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?156views
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.)126views
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>191views
Textbook QuestionFind the length of the remaining side of each triangle. Do not use a calculator.<IMAGE>191views
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 = 48.2121views
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°172views
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°172views
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°182views
Textbook QuestionIn Exercises 14–19, use a sum or difference formula to find the exact value of each expression. cos(45° + 30°)267views
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 meters189views
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°215views
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 meters240views
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°)195views
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 = 10163views
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 = 8153views
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 = 3384views
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 = 50190views
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 feet239views
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 meters245views
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 yards220views
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 2186views
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 2228views
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)161views
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 2190views
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 2186views
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 13195views
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 3264views
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 2206views
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 2218views
Textbook QuestionIn Exercises 69–74, rewrite each expression as a simplified expression containing one term. cos (α + β) cos β + sin (α + β) sin β200views
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