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mathematics
basic technical mathematics

Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions

Use Fig. 2.133. Line CT is tangent to the circle with center at O. Find the indicated angles.∠BTCFig. 2.133 T C B Э A 0 50°
Solve the given problems.In a circle, a chord connects the ends of two perpendicular radii of 6.00 in. What is the area of the minor segment?
Solve the given problems.In Fig. 2.44, if KN = 15,MN = 9, and MO = 12, find LM. L K M Fig. 2.44 N 0
Find all angles of the given measures for the beam support structure shown in Fig. 2.16.110°Figure 2.16 1- A H 20° 50° G -F 20⁰ D DE B C C ZBCHZDCG
Solve the given problems.Each of two walls (with rectangular windows) of an A-frame house has the shape of a trapezoid as shown in Fig. 2.74. If a gallon of paint covers 320 ft2, how much paint is required to paint these walls? 10 ft 3.5 ft 16 ft 12 ft 28 ft Fig. 2.74 10 ft
Solve the given problems.A special wedge in the shape of a regular pyramid has a square base 16.0 mm on a side. The height of the wedge is 40.0 mm. What is the total surface area of the wedge (including the base)?
Use Fig. 2.133. Line CT is tangent to the circle with center at O. Find the indicated angles.∠ABTFig. 2.133 T C B Э A 0 50°
Find all angles of the given measures for the beam support structure shown in Fig. 2.16.115°Figure 2.16 1- A H 20° 50° G -F 20⁰ D DE B C C ZBCHZDCG
Solve the given problems.In Fig. 2.45, if AD = 9 and AC = 12, find AB. В с D Fig.2.45 A
Solve the given problems.Equation (2.9) is c = 2πr. Solve for π, and then use the equation d = 2r, where d is the diameter. State the meaning of the result.
Use Fig. 2.134. Given that AB = 4, BC = 4, CD = 6, and ∠ADC = 53°, find the indicated angle and lengths.∠ABEFig. 2.134 A B E C D
A plane was heading in a direction 58° east of directly north. It then turned and began to head in a direction 18° south of directly east. Find the measure of the obtuse angle formed between the two parts of the trip. See Fig. 2.17.Figure 2.17 58° 18⁰
Solve the given problems.A lawn roller is a cylinder 0.96.0 m long and 0.60 m in diameter. How many revolutions of the roller are needed to roll 76 m2 of lawn?
Solve the given problems.A 1080p high-definition widescreen television screen has 1080 pixels in the vertical direction and 1920 pixels in the horizontal direction. If the screen measures 15.8 in. high and 28.0 in. wide, find the number of pixels per square inch.
Solve the given problems.In Fig. 2.91, for the quarter-circle of radius r, find the formula for the segment area A in terms of r.Fig. 2.91. A = area r ''h
Solve the given problems.In 1897, the Indiana House of Representatives passed unanimously a bill that included “the . . . important fact that the ratio of the diameter and circumference is as five-fourths to four.” Under this definition, what would be the value of π? What is wrong with this
Solve the given problems.A perfect triangle is one that has sides that are integers and the perimeter and area are numerically equal integers. Is the triangle with sides 6, 25, and 29 a perfect triangle?
Use Fig. 2.134. Given that AB = 4, BC = 4, CD = 6, and ∠ADC = 53°, find the indicated angle and lengths.ADFig. 2.134 A B E C D
Solve the given problems.The circumference of a basketball is about 29.8 in. What is its volume?
Solve the given problems.The ratio of the width to the height of a 43.3 cm (diagonal) laptop computer screen is 1.60. What is the width w and height h of the screen?
Solve the given problems.Six equal trapezoidal sections form a conference table in the shape of a hexagon, with a hexagonal opening in the middle. See Fig. 2.75. From the dimensions shown, find the area of the table top.Fig. 2.75. 30.0 in. 60.0 in. 30.0 in. 30.0 in.
Solve the given problems.For the segment in Fig. 2.91, find the segment height h in terms of r.Fig. 2.91. A = area r ''h
Solve the given problems.Government guidelines require that a sidewalk to street ramp be such that there is no more than 1.0 in. rise for each horizontal 20.0 in. of the ramp. How long should a ramp be for a curb that is 4.0 in. above the street?
Use Fig. 2.134. Given that AB = 4, BC = 4, CD = 6, and ∠ADC = 53°, find the indicated angle and lengths.BEFig. 2.134 A B E C D
Solve the given problems.What is the area of a paper label that is to cover the lateral surface of a cylindrical can 3.00 in. in diameter and 4.25 in. high? The ends of the label will overlap 0.25 in. when the label is placed on the can.
Solve for x if (a) ∠A and ∠B are ∠A = (x + 20)° and ∠B = (3x − 2)°. (a) Complementary angles; (b) Alternate-interior angles.
Solve the given problems.The side view of a rivet is shown in Fig. 2.129. It is a conical part on a cylindrical part. Find the volume of the rivet. 0.625 in. || -2.75 in.— 14 1.25 in. 0.625 in. Fig. 2.129
A steam pipe is connected in sections AB, BC, and CD as shown in Fig. 2.18. Find ∠BCD if AB ∥ CD. Fig. 2.18 E--- A B 47° D
Solve the given problems.The angle between the roof sections of an A-frame house is 50°. What is the angle between either roof section and a horizontal rafter?
Use Fig. 2.134. Given that AB = 4, BC = 4, CD = 6, and ∠ADC = 53°, find the indicated angle and lengths.AEFig. 2.134 A B E C D
Solve the given problems.A fenced section of a ranch is in the shape of a quadrilateral whose sides are 1.74 km, 1.46 km, 2.27 km, and 1.86 km, the last two sides being perpendicular to each other. Find the area of the section.
Part of a laser beam striking a surface is reflected and the remainder passes through (see Fig. 2.19). Find the angle between the surface and the part that passes through. Fig. 2.19 Laser beam A- C 28° ABL CO B
Solve the given problems.A person is in a plane 11.5 km above the shore of the Pacific Ocean. How far from the plane can the person see out on the Pacific? (The radius of Earth is 6378 km.)
Solve the given problems.A transmitting tower is supported by a wire that makes an angle of 52° with the level ground. What is the angle between the tower and the wire?
Find the formulas for the indicated perimeters and areas.Perimeter of Fig. 2.135 (a right triangle and semicircle attached) b 2a Fig. 2.135
Solve the given problems.A semicircular patio made of concrete 7.5 cm thick has a total perimeter of 18 m. What is the volume of concrete?
Solve the given problems.A rectangular security area is enclosed on one side by a wall, and the other sides are fenced. The length of the wall is twice the width of the area. The total cost of building the wall and fence is $13,200. If the wall costs $50.00/m and the fence costs $5.00/m, find the
Solve the given problems.The CN Tower in Toronto has an observation deck at 346 m above the ground. Assuming ground level and Lake Ontario level are equal, how far can a person see from the deck? (The radius of Earth is 6378 km.)
Solve the given problems.An 18.0-ft tall tree is broken in a wind storm such that the top falls and hits the ground 8.0ft from the base. If the two sections of the tree are still connected at the break, how far up the tree (to the nearest tenth of a foot) was the break?
An electric circuit board has equally spaced parallel wires with connections at points A, B, and C, as shown in Fig. 2.20. How far is A from C, if BC = 2.15 cm?Figure 2.20 C -B-
Solve the given problems.A ball bearing had worn down too much in a machine that was not operating properly. It remained spherical, but had lost 8.0% of its volume. By what percent had the radius decreased?
Solve the given problems.A dipstick is made to measure the volume remaining in the conical container shown in Fig. 2.130. How far below the full mark (at the top of the container) on the stick should the mark for half-full be placed? 18.0 cm Fig. 2.130 T 12.0 cm
Find the formulas for the indicated perimeters and areas. Perimeter of Fig. 2.136 (a square with a quarter circle at each end) S 1 I Fig. 2.136
Solve the given problems.What is the sum of the measures of the interior angles of a quadrilateral? Explain.
Solve the given problems.A 5G cell tower emits a signal that is clear within 1580 ft of the tower. Can a clear signal be received at a home 1350 ft west and 925 ft south of the tower?
Find the distance on Dundas St. W between Dufferin St. and Ossington Ave. in Toronto, as shown in Fig. 2.21. The north–south streets are parallel.Figure 2.21 Bloor St. W Dundas St. St. Clarens Ave. 550 m 590 m 860 m Dufferin St. Ossington Ave.
Solve the given problems.The Bermuda Triangle is sometimes defined as an equilateral triangle 1600 km on a side, with vertices in Bermuda, Puerto Rico, and the Florida coast. Assuming it is flat, what is its approximate area?
Solve the given problems.Find a formula for the area of a rhombus in terms of its diagonals d1 and d2. (See Exercise 33.)Data from Exercises 33Noting how a diagonal of a rhombus divides an interior angle, explain why the automobile jack in Fig. 2.70 is in the shape of a rhombus. Fig. 2.70
Find the formulas for the indicated perimeters and areas.Area of Fig. 2.135 b 1 2a Fig. 2.135
Solve the given problems related to Fig. 2.22.∠1 + ∠2 + ∠3 = ? B 1 3 N 4 5 D A C Fig. 2.22 AD || BC
Solve the given problems.A circular pool 12.0 m in diameter has a sitting ledge 0.60 m wide around it. What is the area of the ledge?
Solve the given problems.The sail of a sailboat is in the shape of a right triangle with sides of 8.0ft, 15ft, and 17ft. What is the area of the sail?
Find the formulas for the indicated perimeters and areas.Area of Fig. 2.136 S Fig. 2.136
Solve the given problems related to Fig. 2.22.∠4 + ∠2 + ∠5 = ? B 1 3 N 4 5 D A C Fig. 2.22 AD || BC
Solve the given problems.The radius of the Earth’s equator is 3960 mi. What is the circumference?
Solve the given problems.As a ball bearing rolls along a straight track, it makes 11.0 revolutions while traveling a distance of 109 mm. Find its radius.
Solve the given problems.An observer is 550 m horizontally from the launch pad of a rocket. After the rocket has ascended 750 m, how far is it from the observer?
Solve the given problems related to Fig. 2.22.Based on Exercise 48, what conclusion can be drawn about a closed geometric figure like the one with vertices at A, B, and D?Data from Exercises 48∠4 + ∠2 + ∠5 = ? B 1 3 N 4 5 D A C Fig. 2.22 AD || BC
Solve the given problems.The rim on a basketball hoop has an inside diameter of 18.0 in. The largest cross section of a basketball has a diameter of 12.0 in. What is the ratio of the cross-sectional area of the basketball to the area of the hoop?
The angle of elevation is the angle above horizontal that an observer must look to see a higher object. The angle of depression is the angle below horizontal that an observer must look to see a lower object. See Fig. 2.23. Do the angle of elevation and the angle of depression always have the same
Solve the given problems.The beach shade shown in Fig. 2.46 is made up of 30°-60°-90° triangular sections. Find x. (In a 30°-60°-90° triangle, the side opposite the 30° angle is one-half the hypotenuse.) 2.00 m Fig. 2.46 x
Solve the given problems.In a practice fire mission, a ladder extended 10.0 ft just reaches the bottom of a 2.50-ft high window if the foot of the ladder is 6.00 ft from the wall. To what length must the ladder be extended to reach the top of the window if the foot of the ladder is 6.00 ft from the
Answer the given questions.Is a square also a rectangle, a parallelogram, and a rhombus?
Solve the given problems.Suppose that a 5250-lb force is applied to a hollow steel cylindrical beam that has the cross section shown in Fig. 2.92. The stress on the beam is found by dividing the force by the cross-sectional area. Find the stress.Fig. 2.92. 2.25 in. 2222 4.00 in. I
Solve the given problems.With no change in the speed of flow, by what factor should the diameter of a fire hose be increased in order to double the amount of water that flows through the fire hose?
Answer the given questions.If the measures of two angles of one triangle equal the measures of two angles of a second triangle, are the two triangles similar?
Solve the given problems.Using a tape measure, the circumference of a tree is found to be 112 in. What is the diameter of the tree (assuming a circular cross section)?
Solve the given problems.A rectangular room is 18 ft long, 12 ft wide, and 8.0 ft high. What is the length of the longest diagonal from one corner to another corner of the room?
Answer the given questions.If the dimensions of a plane geometric figure are each multiplied by n, by how much is the area multiplied? Explain, using a circle to illustrate.
Solve the given problems.The cross section of a large circular conduit has seven smaller equal circular conduits within it. The conduits are tangent to each other as shown in Fig. 2.93. What fraction of the large conduit is occupied by the seven smaller conduits?Fig. 2.93.
Answer the given questions.What is an equation relating chord segments a, b, c, and d shown in Fig. 2.137. The dashed chords are an aid in the solution.Fig. 2.137 a b C
Find the area of the room in the plan shown in Fig. 2.94. 24 ft -35 ft Fig. 2.94 9.0 ft
Solve the given problems.On a blueprint, a hallway is 45.6 cm long. The scale is 1.2 cm = 1.0 m. How long is the hallway?
Find the length of the pulley belt shown in Fig. 2.95 if the belt crosses at right angles. The radius of each pulley wheel is 5.50 in. хо Fig. 2.95
If the dimensions of a solid geometric figure are each multiplied by n, by how much is the volume multiplied? Explain, using a cube to illustrate.
A 4.0-ft high wall stands 2.0 ft from a building. The ends of a straight pole touch the building and the ground 6.0 ft from the wall. A point on the pole touches the top of the wall. How long is the pole? See Fig. 2.47. Pole Wall - 6.0 ft- Fig. 2.47 4.0 ft 2.0 ft| Building
Solve the given problems.Two parallel guy wires are attached to a vertical pole 4.5 m and 5.4 m above the ground. They are secured on the level ground at points 1.2 m apart. How long are the guy wires?
The two sections of a folding door, hinged in the middle, are at right angles. If each section is 2.5 ft wide, how far are the hinges from the far edge of the other section?
From a common point, two line segments are tangent to the same circle. If the angle between the line segments is 36°, what is the angle between the two radii of the circle drawn from the points of tangency?
Two pipes, each with a 25.0-mm-diameter hole, lead into a single larger pipe (see Fig. 2.96). In order to ensure proper flow, the cross-sectional area of the hole of the larger pipe is designed to be equal to the sum of the cross-sectional areas of the two smaller pipes. Find the inside diameter of
To find the width ED of a river, a surveyor places markers at A, B, C, and D, as shown in Fig. 2.48. The markers are placed such that AB ∥ ED,BC = 50.0 ft ,DC = 312 ft , and AB = 80.0 ft. How wide is the river? E Fig. 2.48 A D B C
A tooth on a saw is in the shape of an isosceles triangle. If the angle at the point is 32°, find the two base angles.
A water pumping station is to be built on a river at point P in order to deliver water to points A and B. See Fig. 2.49. The design requires that ∠APD = ∠BPC so that the total length of piping that will be needed is a minimum. Find this minimum length of pipe. B 6.00 mi 1 CH P - 12.0 mi Fig.
Part of a circular gear with 24 teeth is shown in Fig. 2.97. Find the indicated angle. Fig. 2.97 20°
A lead sphere 1.50 in. in diameter is flattened into a circular sheet 14.0 in. in diameter. How thick is the sheet?
A patio is designed with semicircular areas attached to a square, as shown in Fig. 2.139. Find the area of the patio. p= 18.0 m (for square) i O I I -- Fig. 2.139
The cross section of a drainage trough has the shape of an isosceles triangle whose depth is 12 cm less than its width. If the depth is increased by 16 cm and the width remains the same, the area of the cross section is increased by 160 cm2. Find the original depth and width. See Fig. 2.50. X ↑ -
The velocity of an object moving in a circular path is directed tangent to the circle in which it is moving. A stone on a string moves in a vertical circle, and the string breaks after 5.5 revolutions. If the string was initially in a vertical position, in what direction does the stone move after
A cell phone transmitting tower is supported by guy wires. The tower and three parallel guy wires are shown in Fig. 2.140. Find the distance AB along the tower. 14 m B A 13 m 18 m Fig. 2.140
Find the areas of lots A and B in Fig. 2.141. A has a frontage on Main St. of 140 ft, and B has a frontage on Main St. of 84 ft. The boundary between lots is 120 ft. First Street A Main Street Fig. 2.141 B
A machine part is in the shape of a square with equilateral triangles attached to two sides (see Fig. 2.138). Find the perimeter of the machine part. 2.4 cm Fig. 2.138
A ramp for the disabled is designed so that it rises 0.48 m over a horizontal distance of 7.8 m. How long is the ramp?
To find the height of a flagpole, a person places a mirror at M, as shown in Fig. 2.142. The person’s eyes at E are 160 cm above the ground at A. From physics, it is known that AME = BMF. If AM = 120 cm and MB = 4.5 m, find the height BF of the flagpole. E Mirror A M Fig. 2.142 F B
An airplane is 2100 ft directly above one end of a 9500-ft runway. How far is the plane from the glide-slope indicator on the ground at the other end of the runway?
A rectangular piece of wallboard with two holes cut out for heating ducts is shown in Fig. 2.143. What is the area of the remaining piece? 4.0 ft 8.0 ft Fig. 2.143 1.0 ft 10 1.0 ft 10
A computer screen displays a circle inscribed in a square and a square inscribed in the circle. Find the ratio of (a) The area of the inner square to the area of the outer square, (b) The perimeter of the inner square to the perimeter of the outer square
A typical scale for an aerial photograph is 1/18450. In an 8.00-by 10.0-in. photograph with this scale, what is the longest distance (in mi) between two locations in the photograph?
For a hydraulic press, the mechanical advantage is the ratio of the large piston area to the small piston area. Find the mechanical advantage if the pistons have diameters of 3.10 cm and 2.25 cm
Using aerial photography, the width of an oil spill is measured at 250-m intervals, as shown in Fig. 2.144. Using Simpson’s rule, find the area of the oil spill. Fig. 2.144 190 m -260 m -250 m 220 m 530 m 480 m 320 m 510 m 350 m 730 m 560 m 240 m
The diameter of the Earth is 7920 mi, and a satellite is in orbit at an altitude of 210 mi. How far does the satellite travel in one rotation about the Earth?

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