Exam 3: Additional-Topics-In-Trigonometry

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A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place. ​

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Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 14, b = 7, C = 118° ​ Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 14, b = 7, C = 118° ​   ​

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Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​ A = 20, b = 22, c = 16 ​

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Determine Determine   if   , and   where θ is the angle between u and v.Round answer to two decimal places. if Determine   if   , and   where θ is the angle between u and v.Round answer to two decimal places. , and Determine   if   , and   where θ is the angle between u and v.Round answer to two decimal places. where θ is the angle between u and v.Round answer to two decimal places.

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Find values for b such that the triangle has two solutions. ​ A = 32°, a = 5 ​

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Find the projection of u onto v if Find the projection of u onto v if   ,  , Find the projection of u onto v if   ,

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Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle. ​ A = 9, c = 6, B = 50° ​

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Given a = 11, b = 14, and c = 10, use Heron's Area Formula to find the area of triangle ABC.Round your answer to two decimal places. ​

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Given Given   and   , find   . and Given   and   , find   . , find Given   and   , find   . .

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46 ​Find the projection of u onto v if , 46 ​Find the projection of u onto v if ,   ,   . , 46 ​Find the projection of u onto v if ,   ,   . .

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Given a = 7, b = 10, and c = 11, use the Law of Cosines to solve the triangle for the value of С.Round your answer to two decimal places. Given a = 7, b = 10, and c = 11, use the Law of Cosines to solve the triangle for the value of С.Round your answer to two decimal places.   Figure not drawn to scale Figure not drawn to scale

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Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​ A = 1, b = Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​ A = 1, b =   , c =   ​ , c = Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​ A = 1, b =   , c =   ​

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Find a unit vector in the direction of the given vector. ​ Find a unit vector in the direction of the given vector. ​   ​

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In the figure, α and β are positive angles. ​ In the figure, α and β are positive angles. ​   ​ A = 3, b = 12 Use α = arcsin(0.25sinβ) to write c as a function of β. ​ ​ A = 3, b = 12 Use α = arcsin(0.25sinβ) to write c as a function of β. ​

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Use the dot product to find the magnitude of u if Use the dot product to find the magnitude of u if

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The vector The vector   gives the number of units of two models of laptops produced by a company.The vector   gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 3.5%. gives the number of units of two models of laptops produced by a company.The vector The vector   gives the number of units of two models of laptops produced by a company.The vector   gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 3.5%. gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 3.5%.

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On a map, Orlando is 187 millimeters due south of Niagara Falls, Denver is 282 millimeters from Orlando, and Denver is 244 millimeters from Niagara Falls (see figure).Find the bearing of Denver from Niagara Falls. ​ ​ On a map, Orlando is 187 millimeters due south of Niagara Falls, Denver is 282 millimeters from Orlando, and Denver is 244 millimeters from Niagara Falls (see figure).Find the bearing of Denver from Niagara Falls. ​ ​   ​

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Use the dot product to find the magnitude of u. ​ Use the dot product to find the magnitude of u. ​   ​

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Given that Force 1 = 55 pounds and Force 2 = 130 pounds, find the angle between the forces if the magnitude of the resultant force is 120 pounds.Round your answer to the nearest degree. ​

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Using the figure below, sketch a graph of the given vector.[The graphs in the answer choices are drawn to the same scale as the graph below.] ​ Using the figure below, sketch a graph of the given vector.[The graphs in the answer choices are drawn to the same scale as the graph below.] ​     ​ Using the figure below, sketch a graph of the given vector.[The graphs in the answer choices are drawn to the same scale as the graph below.] ​     ​

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