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Drawing Denso QR Bar Code in .NET framework Solution of Right Triangles

CHAPTER 4 Solution of Right Triangles
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Show that the base b of an isosceles triangle whose equal sides are a and whose vertex angle is is given by b 1 2a sin 2u. Show that the perimeter P of a regular polygon of n sides inscribed in a circle of radius r is given by P (180 /n). 2nr sin
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A wheel 5 ft in diameter rolls up an incline of 18 20 . What is the height of the center of the wheel above the base of the incline when the wheel has rolled 5 ft up the incline Ans. 3.95 ft
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A wall is 10 feet tall and is 15 feet from a house. A window in the house is 30.5 feet above the ground. A fire escape slide attaches to the bottom of the window and to the top of the wall opposite the window. How long a slide must be purchased Ans. 25.4 ft
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A parked car is spotted from a hotel window which is 100 m above the car. If the angle of depression from the window to the car is 15.4 , how far is the car from the window Ans. 377 m
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A tower 45 m high casts a shadow of 12 m. What is the angle of elevation of the sun Ans. 75
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A rectangle is 48 cm long and 34 cm wide. What is the angle the diagonal makes with the longer side Ans. 35
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A railroad track makes an angle of 4.8 with the horizontal. How far must the train go up the track for it to gain 30 m in altitude Ans. 359 m
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Practical Applications
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5.1 Bearing
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The bearing of a point B from a point A in a horizontal plane is usually defined as the angle (always acute) made by the ray drawn from A through B with the north-south line through A. The bearing is then read from the north or south line toward the east or west. The angle used in expressing a bearing is usually stated in degrees and minutes. For example, see Fig. 5.1.
Fig.5.1
In aeronautics, the bearing of B from A is more often given as the angle made by the ray AB with the north line through A, measured clockwise from the north (i.e., from the north around through the east). For example, see Fig. 5.2.
Fig. 5.2
CHAPTER 5 Practical Applications
5.2 Vectors
Any physical quantity, like force or velocity, which has both magnitude and direction is called a vector quantity. A vector quantity may be represented by a directed line segment (arrow) called a vector. The direction of the vector is that of the given quantity and the length of the vector is proportional to the magnitude of the quantity.
EXAMPLE 5.1 An airplane is traveling N40 E at 200 mi/h. Its velocity is represented by the vector AB in Fig. 5.3.
Fig. 5.3 EXAMPLE 5.2 A motor boat having the speed 12 mi/h in still water is headed directly across a river whose current is 4 mi/h. In Fig. 5.4, the vector CD represents the velocity of the current and the vector AB represents, to the same scale, the velocity of the boat in still water. Thus, vector AB is three times as long as vector CD.
Fig. 5.4 EXAMPLE 5.3 In Fig. 5.5, vector AB represents a force of 20 lb making an angle of 35 with the positive direction on the x axis and vector CD represents a force of 30 lb at 150 with the positive direction on the x axis. Both vectors are drawn to the same scale.
Fig. 5.5
Two vectors are said to be equal if they have the same magnitude and direction. A vector has no fixed position in a plane and may be moved about in the plane provided that its magnitude and direction are not changed.
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