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An airplane travels 15,000 ft through the air at a uniform angle of climb, thereby gaining 1900 ft in altitude. Find its angle of climb. (8.7) Sighting to the top of a monument. William found the angle of elevation to measure 16 (Fig. 8-20). The ground is level, and the transit is 5 ft above the ground. If the monument is 86 ft high, find, to the nearest foot, the distance from William to the foot of the monument. (8.8)

Fig. 8-20



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The major differences between stocks and bonds may be summarized as follows: Stocks 1. Representation Ownership in the corporation 2. Inducement to Holders Dividends 3. Accounting Treatment Dividends are a distribution of pro ts; stocks are equity 4. Repayment By selling in the market at any time Bonds 1. Representation A debt of the corporation 2. Inducement to Holders Interest 3. Accounting Treatment Interest is an expense; bonds are a longterm liability 4. Repayment On a predetermined date

The following are the derived datatypes de ned by the datatypes document: normalizedString token language ID IDREF IDREFS ENTITY ENTITIES NMTOKEN NMTOKENS

Find to the nearest degree the measure of the angle of elevation of the sun when a tree 60 ft high casts a shadow of (a) 10 ft; (b) 60 ft.





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At a certain time of day, the angle of elevation of the sun measures 34 . Find, to the nearest foot, the length of the shadow cast by (a) a 15-ft vertical pole; (b) a building 70 ft high. (8.8) A light at C is projected vertically to a cloud at B. An observer at A, 1000 ft horizontally from C, notes the angle of elevation of B. Find the height of the cloud, to the nearest foot, if m A 37 . (8.8) A lighthouse built at sea level is 180 ft high (Fig. 8-21). From its top, the angle of depression of a buoy measures 24 . Find, to the nearest foot, the distance from the buoy to the foot of the lighthouse. (8.8)

Fig. 8-21

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An observer, on top of a hill 300 ft above the level of a lake, sighted two ships directly in line. Find, to the nearest foot, the distance between the boats if the angles of depression noted by the observer measured (a) 20 and 15 ; (b) 35 and 24 ; (c) 9 and 6 . (8.10) In Fig. 8-22, m A 43 , m BDC 54 , m C the result of (a), find the length of AB. 90 , and DC 170 ft. (a) Find the length of BC. (b) Using (8.10)

Fig. 8-22

Fig. 8-23

Tangents PA and PB are drawn to a circle from external point P. m APB nearest tenth the radius of the circle.

Summary

A square unit is the surface enclosed by a square whose side is 1 unit (Fig. 9-1). The area of a closed plane figure, such as a polygon, is the number of square units contained in its surface. Since a rectangle 5 units long and 4 units wide can be divided into 20 unit squares, its area is 20 square units (Fig. 9-2). The area of a rectangle equals the product of the length of its base and the length of its altitude (Fig. 9-3). Thus if b 8 in and h 3 in, then A 24 in2. The area of a square equals the square of the length of a side (Fig. 9-4). Thus if s 6, then A s2 36. It follows that the area of a square also equals one-half the square of the length of a diagonal. Since A s2 and s d / !2, A 1 d 2. 2 Note that we sometimes use the letter A for both a vertex of a figure and its area. You should have no trouble determining which is meant. The reader should feel free to use a calculator for the work in this chapter.

Fig. 9-1

Fig. 9-2

Fig. 9-3

Fig. 9-4

9.1 Area of a rectangle (a) Find the area of a rectangle if the base has length 15 and the perimeter is 50. (b) Find the area of a rectangle if the altitude has length 10 and the diagonal has length 26. (c) Find the lengths of the base and altitude of a rectangle if its area is 70 and its perimeter is 34.

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