MAT 105 TEST 3 REVIEW (CHAP 2 & 4) NAME Solve the problem. 1) Given that AB DC & AD BC, find the measure of angle x. 124 2) Find the supplement of 38. 3) Find the complement of 45. 4) Find the measure of angle x. x y 102 5) If Main Street is parallel to First Street, find the value of x. 396 m 296 m 235 m 1
6) A part used in manufacturing is shown in the figure. If the upper and lower sections are parallel, what is the angle between the diagonal and the upper section? 37 7) Trusses are often used in the construction of buildings. If DAB = 42 what is the measure of BDF in the truss shown below. 8) Two angles of a triangle are 36 and 96. Find the third angle. 9) One of the base angles of an isosceles triangle is 23. Find the measures of the other two angles. 10) Find A. 19 in 154 19 in 2
11) Determine the measure of angle x. 47 x 29 40 81 Find the perimeter. 12) 19 ft 18 ft 27 ft Find the area. 13) 24 yd 21 yd 45 yd 14) a = 31 ft, b = 43 ft, c = 37 ft 3
Find the missing length in the right triangle. 15) 3.0 in. 7.0 in. 16) 9.0 mi 20 mi 17) The hypotenuse of a right triangle is 78.4 in. and one leg is 29.3 in. Find the length of the other leg. Solve the problem. Round your result to an appropriate number of significant digits. 18) In order to measure the distance across a pond (from A to D), Maria made the measurements shown in the drawing. What is the distance? A C 54 yd E 51 47 yd 51 166 yd 48 yd D B 19) A church steeple casts a shadow 102 ft long, and at the same time a 8.00-ft post cast a shadow 5.00 ft long. How high is the steeple? 4
20) A line from the top of a cliff to the ground passes just over the top of a pole 5.0 ft high and meets the ground at a point 9.0 ft from the base of the pole. If the point is 74 ft from the base of the cliff, how high is the cliff? 21) Joe has a pennant for the University of Michigan. It is in the shape of an isosceles triangle. If each equal side is 71.0 cm and the third side is 26.0 cm, what is the area of the pennant? 22) A rectangular classroom is 11.0 ft wide, 19.0 ft long, and 8.50 ft high. What is the length of the longest diagonal from one corner to another corner of the room? Solve the problem. 23) Find the perimeter of a rhombus with a side of 1.59 mm. 24) Find the perimeter of a rectangle with length of 48.78 cm and width of 73.01 cm. 25) Find the perimeter of an isosceles trapezoid with short base of 11.3 cm, long base of 25.5 cm, and height of 40.9 cm. 26) Find the perimeter of a parallelogram with bases of 69.3 in. and 33.4 in. and height of 15.6 in. 5
27) Find the area of a square with side of 6.9 cm. 28) Find the area of a parallelogram with a base of 78 cm and a height of 36 cm. 29) Find the area of a trapezoid with short base of 76 yd, long base of 93 yd, and height of 14 yd. 30) A one-story building is 248 ft by 255 ft. If a square patio with sides 21 ft occupies the center of the building, how much area remains for offices? 31) A field is in the shape of a parallelogram with sides of length 279.0 ft and 29.15 ft. The altitude to the longer side is 24.61 ft. Find the length of fencing which must be purchased to enclose the entire field. 32) A newly built house has a room in it such that the length is 3.3 ft more than the width. The perimeter is 39.4 ft. What are the dimensions? 33) A home has a living room that is 15 ft wide and 18 ft long. The height is 9 ft. Bob needs to paint the room. He has to paint the walls and the ceiling. (He will not paint the floor.) There are two 3.0 ft by 5.0 ft windows and a 4.0 ft by 7.0 ft opening into the room that will not be painted. A gallon of paint covers 320 ft2. How many gallons of paint (to the nearest tenth) are needed? (All data are accurate to two significant figures.) 6
Find the circumference of the circle with the given radius or diameter. 34) r = 0.315 in. 35) d = 4.55 cm Find the area of the circle. 36) A circle with diameter 11.2 ft Determine the indicated arc or angle. 37) FindBC. 64 52 38) Find ADB. 70 56 39) Find ABC. 66 52 7
40) Find AC. 70 41) Find CAB. 74 42) Find ACB. 64 Solve the problem. 43) A small circular pool is enclosed in a square. Find the area inside the square but outside the circle. 3.6 m 44) Find the shaded area in the figure. 7.17 cm 8
45) Semicircles are placed on the sides of an equilateral triangle with sides 6.04 ft as shown. Find the shaded area. 46) A bicycle tire has a radius of 13.8 in. How far will it travel in 189 revolutions? 47) The circumference of a tree is found to be 118 in. What is its radius? 48) A washer has an inner radius of 0.23 in. and an outer radius of 0.48 in. Find the area of the washer. Find the volume. 49) A cube measuring 21 m on each edge 50) Radius = 4.5 in., height = 11 in. 9
Find the volume. 51) A sphere with diameter 7.5 cm 52) A cone with height 3.9 cm and diameter 5.9 cm 53) A triangular pyramid with base area 18.6 ft2 and height 3.0 ft 54) A rectangular pyramid with base area 19.4 m2 and height 3.0 m Solve the problem. 55) Find the total surface area of a box 22 cm by 21.9 cm by 14 cm. 56) Find the total surface area of a cube with an edge of 18 ft. 57) Find the total surface area of a right circular cylinder with d = 9.2 m, h = 5.3 m. 58) Find the total surface area of a right circular cone with diameter 16.6 ft and height 13.9 ft. 10
59) Find the lateral surface area of a regular pyramid with a perimeter of 3.81 ft and a slant height of 2.47 ft. 60) A cylindrical drain pipe is 7.0 inches across the top and about 11 inches high. How many cubic inches of water could it hold? 61) A dog toy is constructed in the shape of a cylinder with a length of 6.8 in. The cylinder has a hemishpere at each end. The diameter is 1.6 in. Find the total volume. 11
Given that is an acute angle, find the five remaining trig function values of. DO NOT USE INVERSE FUNCTIONS. 62) sin = 3 4 (Exact values in simplest radical form) 63) cos = 9 10 (Exact values in simplest radical form) 64) tan = 0.3846. (To 4 sig digits) Use a calculator to find the function value. Give answer to three sig digits. 65) sin 46.6. 66) cos 13.7 67) cot 17.9 12
Determine in decimal degrees, given 0 90. Round results to an appropriate number of significant digits. 68) sin = 0.402 69) cos = 0.29 Determine in decimal degrees, given 0 90. Round results to an appropriate number of significant digits. 70) tan = 0.093 71) csc = 3.63 72) sec = 1.8 73) cot = 2.109 Find the requested function value of to 4 sig digits. 74) If sin = 0.3571, find sec. 75) If cos = 0.8571, find tan. 76) Find cot, if tan = 0.3037. 13
Solve the problem. 77) The equation P = IV cos gives the power (in watts) absorbed in an ac circuit. Find when P = 110 W, V = 120 V, and I = 1.4 A. Round results to nearest degree. Find the requested part of the triangle. 78) Find the measure of the angle A to the nearest tenth of a degree. 11.5 17.7 79) Find the measure of the angle A to the nearest tenth of a degree. 6.72 6.10 80) Find the measure of the side labeled x to three sig digits. 38.7 x 1770 14
Find the indicated part of the right triangle. 81) One leg is 20.7, and the hypotenuse is 43.9. Find the smaller acute angle. Round your answer to the nearest tenth of a degree. 82) One leg is 7.80, and the angle opposite this leg is 54.5. Find the other leg. Round your answer to three sig digits. 83) The legs are 5.1 and 9.9. Find the larger acute angle. Round your answer to the nearest degree. Determine the value of x or as requested. 84) Determine the value of to the nearest degree. 27 ft 54 ft 15
Solve the right triangle. Round results to an appropriate number of significant digits. 85) a = 1.3 cm, b = 1.1 cm 86) a = 3.90 m, B = 26.0 87) B = 20.6, c = 3.41 mm 16
Solve the problem. 88) From a balloon 1090 ft high, the angle of depression to the ranger headquarters is 51.6. How far is the headquarters from a point on the ground directly below the balloon (to 3 sig digits)? 89) From a boat on the lake, the angle of elevation to the top of a cliff is 14.5. If the base of the cliff is 2270 ft from the boat, how high is the cliff? (to 3 sig digits) 90) When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 36.7. If Joey is known to be standing 10.0 ft from the base of the tree, how tall is the tree (to 3 sig digits)? 91) A plane is found by radar to be flying 5.60 km above the ground. The angle of elevation from the radar to the plane is 82.6. Ten seconds later, the plane is directly over the station. Find the speed of the plane, to 3 sig digits, assuming that it is flying level. 17