Practice Problems Test 3

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1 Pactice Poblems Test ********************************************************** ***NOTICE - Fo poblems involving ʺSolve the Tiangleʺ the angles in this eview ae given by Geek lettes: A = α B = β C = γ So, solution sets will look like this: With alphabetical angels: A = a = B = b = C = c = With Geek letteed angles: α = a = β = b = γ = c = ********************************************************* 7) B = 0 b = a = 8) B = 9 b = 8.9 a =.67 9) C = a = 8.7 c = 6. Solve the poblem. 0) A suveyo standing metes fom the base of a building measues the angle to the top of the building and finds it to be 7. The suveyo then measues the angle to the top of the adio towe on the building and finds that it is 0. How tall is the adio towe? Solve the ight tiangle using the infomation given. Round answes to two decimal places, if necessay. ) b = 8, α = 0 ; find a, c, and β Solve the tiangle. Round any answes to decimal places. ) α = 0, β = 0, a = Fo #ʹs - 7, two sides and an angle ae given. Detemine whethe the given infomation esults in one tiangle, two tiangles, o no tiangle at all. Solve any tiangle(s) that esults. Round any answes to decimal places. ) a = 7, b = 9, β = 9 ) a = 8, b = 6, β = ) a =, b =69, α = 6 Two sides and an angle (SSA) of a tiangle ae given. Detemine whethe the given measuements poduce one tiangle, two tiangles, o no tiangle at all. Solve each tiangle that esults. Round lengths to the neaest tenth and angle measues to the neaest degee. 6) A = 0 a = 8 b = 6 ) A ship sailing paallel to shoe sights a lighthouse at an angle of fom its diection of tavel. Afte taveling miles fathe, the angle is. At that time, how fa is the ship fom the lighthouse? ) A guy wie to the top of a towe makes an angle of with the level gound. At a point feet fathe fom the base of the towe and in line with the base of the wie, the angle of elevation to the top of the towe is. What is the length of the guy wie? Find the aea of the tiangle having the given measuements. Round to the neaest squae unit. ) A = 7 b = in. c = 7 in. ) A = b = 7 m c = 7 m ) b = in. A = 8 C = 7 6) b = 0 ft A = 8 C = 96

2 Solve the tiangle. Round lengths to the neaest tenth and angle measues to the neaest degee. 7) C = a = 8 b = Use a pola coodinate system to plot the point with the given pola coodinates. 7) (, - π ) 8) B = 6 a = c = 8 9) C = 0 b = a = 0) a = 7 b = c = 6 Solve the poblem. ) Two sailboats leave a habo in the Bahamas at the same time. The fist sails at mph in a diection 0. The second sails at mph in a diection 90. Assuming that both boats maintain speed and heading, afte hous, how fa apat ae the boats? 8) (-, ) ) Two points A and B ae on opposite sides of a building. A suveyo selects a thid point C to place a tansit. Point C is 6 feet fom point A and 66 feet fom point B. The angle ACB is. How fa apat ae points A and B? ) The distance fom home plate to dead cente field in Sun Devil Stadium is 0 feet. A baseball diamond is a squae with a distance fom home plate to fist base of 90 feet. How fa is it fom fist base to dead cente field? 9) (, ) Use Heonʹs fomula to find the aea of the tiangle. Round to the neaest squae unit. ) a = 7 cm b = 6 cm c = cm ) a = 7 in b = in c = in 6) a = in b = m c = 7 m

3 0) (-, 690 ) ) (, 0 ) ) (, -0 ) ) (0, ) ) (, 7π 6 ) ) (, 60 ) Find anothe epesentation, (, θ), fo the point unde the given conditions. 6) 6, π, > 0 and π < θ < π

4 7), π, < 0 and 0 < θ < π The gaph of a pola equation is given. Select the pola equation fo the gaph. ) 8) 9, π 6 9) 8, π 6, > 0 and -π < θ < 0, < 0 and π < θ < π Pola coodinates of a point ae given. Find the ectangula coodinates of the point. 0) 7, π ) 9, π A) sin θ = - B) = - sin θ C) = - D) = - cos θ ) (-, 0 ) ) (, - ) ) (-, 60 ) ) ) (-, 6 ) The ectangula coodinates of a point ae given. Find the pola coodinates of the point. 6) (, 0) ) (0, -) A) = cos θ B) = + cos θ C) = sin θ D) = + sin θ 8) (, ) ) 9) (, ) 0) (9, -9) A) = + cos θ B) = 8 cos θ C) = + sin θ D) = 8 sin θ

5 ) 6) w A) = sin(θ) B) = cos(θ) C) = D) = + cos(θ) Use the figue below. Detemine whethe the given statement is tue o false. Use the vectos in the figue below to gaph the following vecto. 7) G + H = F 8) A + B + C + D + E = 0 ) u + z The vecto v has initial position P and teminal point Q. Wite v in the fom ai + bj; that is, find its position vecto. 9) P = (0, 0); Q = (-, -) 60) P = (, ); Q = (-, -) 6) P = (-, -); Q = (, ) Find the indicated quantity. 6) u = i - j, v = -9i + 8j; Find u + v. 6) u = -0i - j, v = i + 7j; Find u - v. 6) If w = i + j, find w. 6) If v = i - j and w = - 7i + j, find v -w. 66) If v = i - j, find v. 67) If v = -7i + j and w = i + j, find v + w. Find the quantity if v = i - 7j and w = i + j. 68) v + w

6 Wite the vecto v in the fom ai + bj, given its magnitude v and the angle α it makes with the positive x-axis. 69) v =, α = 0 70) v = 0, α = 7) v = 7, α = 0 Find the dot poduct v.w. 7) v = i + j, w = -i + j 7) v = i, w = j 7) v = -i + 9j, w = -i - 6j Find the angle between v and w. Round you answe to one decimal place, if necessay. 7) v = i - 9j, w = -i - j 86) A peson is pulling a feight cat with a foce of pounds. How much wok is done in moving the cat 90 feet if the catʹs handle makes an angle of 7 with the gound? 87) The magnitude and diection of two foces acting on an object ae pounds, N E, and pounds, S0 E, espectively. Find the magnitude, to the neaest hundedth of a pound, and the diection angle, to the neaest tenth of a degee, of the esultant foce. 88) Two foces, F and F, of magnitude 60 and 70 pounds, espectively, act on an object. The diection of F is N0 E and the diection of F is N0 W. Find the magnitude and the diection angle of the esultant foce. Expess the diection angle to the neaest tenth of a degee. 76) v = -i + 7j, w = -6i - j 77) v = i, w = j State whethe the vectos ae paallel, othogonal, o neithe. 78) v = i + j, w = i - j 79) v = i + j, w = i - j 80) v = i - j, w = i - j 8) v = i + j, w = 6i + 8j 8) v = i + j, w = i + j 8) v = i + j, w = i - j Solve the poblem. 8) Find the wok done by a foce of pounds acting in the diection of 9 to the hoizontal in moving an object 8 feet fom (0, 0) to (8, 0). Round answe to the neaest tenth of a foot-pound. 8) A wagon with a ope tied to it is pulled hoizontally by exeting a foce of 60 pounds at an angle of with the hoizontal. To the neaest tenth of a foot-pound, how much wok is done in moving the wagon 0 feet? 6

7 Answe Key Testname: REVIEWTSUM0 ) a = 6.7 c = 0. β = 0 ) γ = 00, b =.6, c =.9 ) one tiangle α =.9, γ = 9.06, c =.88 ) two tiangles α = 0.9, γ =.8, c =.6 o α = 9.8, γ =.9, c =. ) one tiangle α =.9, γ = 9.06, c =.88 6) B = 90, C = 60, c =.9 7) no tiangle 8) A = 0, C =, c = 0.6; A = 0, C =, c =. 9) A =, B = 0, b = 7.; A = 8, B = 7, b =. 0). metes ).96 miles ) 7.69 feet ) 7 in. ) m ) 8 in. 6) 7 ft 7) c =.8, A = 8, B = 0 8) b =.0, A = 76, C = 9) c =., A =, B = 7 0) A = 6, B = 6, C = 9 ) 98. miles ) 6.7 feet ) 6. feet ) 0 cm ) 8 in 6) m 7

8 Answe Key Testname: REVIEWTSUM0 7) 8) 9)

9 Answe Key Testname: REVIEWTSUM0 0) ) )

10 Answe Key Testname: REVIEWTSUM0 ) ) ) ) 6, 9 π 7) -, π 8) 9, - 6 π 0

11 Answe Key Testname: REVIEWTSUM0 9) -8, 9 6 π 0) - 7, 7 ) ) ) -9, 9, - -, - ) (-, 0) ) (-.0, -.99) 6) (, 0) 7) (, - π ) 8) (, π ) 9) (, π 6 ) 0) (9, 7π ) ) B ) D ) A ) B )

12 Answe Key Testname: REVIEWTSUM0 6) 7) False 8) Tue 9) v = -i - j 60) v = -7i - j 6) v = i + 7j 6) -6i + j 6) -i - 9j 6) 0i + 6j 6) 7i -j 66) 67) 68) ) v = - i - j 70) v = 0 - i + j 7) v = 7 i + j 7) 0 7) 0 7) 0 7) 7. 76) ) 90 78) othogonal 79) othogonal 80) paallel 8) paallel 8) neithe 8) neithe 8). ft-lb 8) 000 cos( ) 78.9 ft-lb 86) 87.8 ft-lb 87) F = 7.0; θ = ) F = 99.7; θ = 9.7

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Math Pecalculus Ch. 6 Review Name SHORT ANSWER. Wite the wod o phase that best completes each statement o answes the question. Solve the tiangle. ) ) 6 7 0 Two sides and an angle (SSA) of a tiangle ae