MATH 1040 CP 15 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Transcription

1 MATH 1040 CP 15 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the triangle. 1) 1) Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 2) A = 26, B = 51, c = 27 2) 3) A = 11.2, C = 131.6, a = ) Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree. 4) A = 30, a = 21, b = 42 4) 5) C = 35, a = 18.7, c = ) 6) B = 41, a = 4, b = 3 6) Find the area of the triangle having the given measurements. Round to the nearest square unit. 7) C = 115, a = 4 yards, b = 5 yards 7) 8) A = 27, b = 14 inches, c = 5 inches 8) Solve the problem. 9) A surveyor standing 52 meters from the base of a building measures the angle to the top of the building and finds it to be 36. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 48. How tall is the radio tower? 9) 10) A guy wire to a tower makes a 70 angle with level ground. At a point 39 ft farther from the tower than the wire but on the same side as the base of the wire, the angle of elevation to the top of the tower is 35. Find the length of the wire (to the nearest foot). 10) 1

2 Find a. If necessary, round your answer to the nearest hundredth. 11) 11) Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 12) 12) ) a = 9, b = 13, c = 16 13) 14) b = 2, c = 3, A = 85 14) 15) a = 12, b = 12, c = 11 15) 16) a = 8, b = 6, c = 4 16) Solve the problem. 17) A plane flying a straight course observes a mountain at a bearing of 31.3 to the right of its course. At that time the plane is 8 kilometers from the mountain. A short time later, the bearing to the mountain becomes How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a km)? 17) 18) Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit. Point C is 52 feet from point A and 74 feet from point B. The angle ACB is 51. How far apart are points A and B? 18) 19) A painter needs to cover a triangular region 62 meters by 67 meters by 73 meters. A can of paint covers 70 square meters. How many cans will be needed? 19) Use Heron's formula to find the area of the triangle. Round to the nearest square unit. 20) a = 17 yards, b = 17 yards, c = 17 yards 20) 21) a = 8 inches, b = 14 inches, c = 8 inches 21) 2

3 Match the point in polar coordinates with either A, B, C, or D on the graph. 22) -2, ) Find another representation, (r, ), for the point under the given conditions. 23) 8, 6, r > 0 and -2 < < 0 23) Polar coordinates of a point are given. Find the rectangular coordinates of the point. 24) (-3, -135 ) 24) 25) 4.5, 9 25) 26) 7, ) The rectangular coordinates of a point are given. Find polar coordinates of the point. Express in radians. 27) (7, -7) 27) 28) (5, -5) 28) 29) (-2 2, -2 2) 29) 30) (-5, 0) 30) Convert the rectangular equation to a polar equation that expresses r in terms of. 31) 8x - 7y + 10 = 0 31) 32) x = 6 32) 33) y 2 = 3x 33) 3

4 Convert the polar equation to a rectangular equation. Then determine the graph's slope and y-intercept. 34) r sin - 4 = 8 34) Convert the rectangular equation to a polar equation that expresses r in terms of. 35) (x - 13)2 + y 2 = ) Convert the polar equation to a rectangular equation. 36) = ) 37) r = 2 37) 38) r 2 sin 2 = 9 38) 39) r = 6 cos + 4 sin 39) 40) r = -5 cos 40) Convert the polar equation to a rectangular equation. Then determine the graph's slope and y-intercept. 41) r cos + 6 = ) Solve the problem. 42) The wind is blowing at 10 knots. Sailboat racers look for a sailing angle to the 10-knot wind that produces maximum sailing speed. In this application, (r, ) describes the sailing speed r, in knots, at angle to the 10-knot wind. Four points in this 10-knot-wind situation are (6.3, 50 ), (7.2, 95 ), (7.3, 120 ) and (7.1, 135 ). Based on theses points, which sailing angle to the 10-knot wind would you recommend to a serious sailboat racer? What sailing speed is achieved at this angle? 42) Test the equation for symmetry with respect to the given axis, line, or pole. 43) r = 2 cos ; the polar axis 43) 44) r = cos ; polar axis 44) 45) r 2 = sin 2 ; the pole 45) 4

5 Graph the polar equation. 46) r = 4 sin 46) 47) r = 3 + sin 47) 48) r = 3 - cos 48) 5

6 49) r 2 = 4 cos (2 ) 49) 50) r = 3 sin 2 50) 51) r = sin 2 51) 6

7 Answer Key Testname: MATH1040CP16 1) B = 45, a = 8.11, c = ) C = 103, a = 12.1, b = ) B = 37.2, b = 289.2, c = ) B = 90, C = 60, c = ) A1 = 42, B1 = 103, b1 = 27.4; A2 = 138, B2 = 7, b2 = 3.4 6) A1 = 61, C1 = 78, c1 = 4.5; A2 = 119, C2 = 20, c2 = 1.6 7) 9 square yards 8) 16 square inches 9) meters 10) 39 feet 11) ) A = 109, B = 39, C = 32 13) A = 34, B = 54, C = 92 14) a = 3.5, B = 35, C = 60 15) A = 63, B = 63, C = 54 16) A = 104, B = 47, C = 29 17) 6.3 kilometers 18) 57.8 feet 19) 28 cans 20) 125 square yards 21) 30 square inches 22) A 23) 8, ) 3 2 2, ) (-0.8, 4.4) 26) - 7 2, ) 7 2, ) (-5 2, 135 ) 29) (4, 225 ) 30) (5, ) ) r = (8 cos - 7 sin ) 32) r = 6 cos 33) r = 3 cot x cscx 34) y = x + 8 2; slope: 1; y-intercept: ) r = 26 cos 36) y = - 3x 37) x 2 + y 2 = 4 7

8 Answer Key Testname: MATH1040CP16 38) xy = ) x 2 + y 2 = 6x + 4y 40) x y 2 25 = ) y = x 3-9; slope: 3; y-intercept: -9 42) 120 ; 7.3 knots 43) has symmetry with respect to polar axis 44) has symmetry with respect to the polar axis 45) has symmetry with respect to the pole 46) 47) 48) 8

9 Answer Key Testname: MATH1040CP16 49) 50) 51) 9