auto generate barcode vb net To three significant digits, the radius r of the 40th parallel is 3030 mi. in Visual Studio .NET

Generation QR in Visual Studio .NET To three significant digits, the radius r of the 40th parallel is 3030 mi.

To three significant digits, the radius r of the 40th parallel is 3030 mi.
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Fig. 4.6
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CHAPTER 4 Solution of Right Triangles
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4.11 Find the perimeter of a regular octagon inscribed in a circle of radius 150 cm.
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In Fig. 4.7, two consecutive vertices A and B of the octagon are joined to the center O of the circle. The triangle OAB is isosceles with equal sides 150 and / AOB 360 /8 45 . As in Prob. 4.9, we bisect / AOB to form the right triangle MOB. Then MB OB sin / MOB 150 sin 22 30 150(0.3827) 57.4, and the perimeter of the octagon is 16MB 16(57.4) 918 cm.
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1 M 22 2 1 22 2 150
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4.12 To find the width of a river, a surveyor set up his surveying equipment at C on one bank and sighted across to a point B on the opposite bank; then, turning through an angle of 90 , he laid off a distance CA 225 m. Finally, setting the equipment at A, he measured / CAB as 48 20 . Find the width of the river.
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See Fig. 4.8. In the right triangle ACB, CB AC tan / CAB 225 tan 48 20 225(1.1237) 253 m
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Fig. 4.8
4.13 In Fig. 4.9, the line AD crosses a swamp. In order to locate a point on this line, a surveyor turned through an angle 51 16 at A and measured 1585 feet to a point C. He then turned through an angle of 90 at C and ran a line CB. If B is on AD, how far must he measure from C to reach B
CB AC tan 51 16 1585(1.2467) 1976 ft
Fig. 4.9
CHAPTER 4 Solution of Right Triangles
4.14 From a point A on level ground, the angles of elevation of the top D and bottom B of a flagpole situated on the top of a hill are measured as 47 54 and 39 45 . Find the height of the hill if the height of the flagpole is 115.5 ft. (See Fig. 4.10.)
Manual: Let the line of the pole meet the horizontal through A in C. In the right triangle ACD, AC In the right triangle ACB, AC Then (115.5 BC)(0.9036) DC cot 47 54 BC cot 39 45 BC(1.2024) 115.5(0.9036) 1.2024 0.9036 DC/tan 47 54 BC/tan 39 45 . (115.5 BC)(0.9036). BC(1.2024).
349.283 (DB BC)/tan 47 54 .
Calculator: In the right triangle ACD, AC In the right triangle ACB, AC
Fig. 4.10
Then
BC tan 39 45r BC tan 47 54 BC tan 47 54 (tan 47 54 BC tan 39 45 tan 39 45 )BC BC
DB BC tan 47 54r DB tan 39 45 DB tan 39 45 DB tan 39 45 DB tan39 45r tan47 54r tan39 45r 45>60) 115.5tan (39 tan (47 54>60) tan (39 45>60) 349.271 BC tan 39 45
The height of the hill is 349.3 ft.
4.15 From the top of a lighthouse, 175 ft above the water, the angle of depression of a boat due south is 18 50 . Calculate the speed of the boat if, after it moves due west for 2 min, the angle of depression is 14 20 .
In Fig. 4.11, AD is the lighthouse, C is the position of the boat when due south of the lighthouse, and B is the position 2 min later.
CHAPTER 4 Solution of Right Triangles
Fig. 4.11
Manual: In the right triangle CAD, AC In the right triangle BAD, AB In the right triangle ABC, BC Calculator: In the right triangle CAD, AC In the right triangle BAD, AB In the right triangle ABC, BC BC
AD cot / ACD AD cot / ABD 2(AB)2 (AC)2
175 cot 18 50 175 cot 14 20 2(685)2
175(2.9319) 175(3.9136) (513)2 453.6
513. 685.
175/tan 18 50 . 175/tan 14 20 . 2(AB)2 (AC)2. [175>tan (18 50>60) ]2
2[1175>tan (14 453.673
20>60) ]2
The boat travels 454 ft in 2 min; its speed is 227 ft/min.
SUPPLEMENTARY PROBLEMS
4.16 Find, to four decimal places, the values of the six trigonometric functions of each of the following angles: (a) 18 47 , Ans. (a) (b) (c) (d) 18 47 32 13 58 24 79 45 (b) 32 13 , sine 0.3220 0.5331 0.8517 0.9840 (c) 58 24 , cosine 0.9468 0.8460 0.5240 0.1780 (d) 79 45 tangent 0.3401 0.6301 1.6255 5.5304 cotangent 2.9403 1.5869 0.6152 0.1808 secant 1.0563 1.1820 1.9084 5.6201 cosecant 3.1057 1.8757 1.1741 1.0162 0.1779,
[NOTE: With a calculator, the values are the same except for (a) cos 18 47 (d) tan 79 45 5.5301, and (d) sec 79 45 5.6198.]
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