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Issue at Par When a corporation is organized, the charter will state how many shares of common and preferred stock are authorized. Often more stock is au thorized than is intended to be sold immediately. This will enable the cor poration to expand in the future without applying to the state for permission to issue more shares. When stock is sold for cash and issued immedi ately, the entry to record the security has the usual form: Cash is debited, and the particular security is credited. A corporation may accept property oth er than cash in exchange for stock. If this occurs, the assets should be recorded at fair market value, usually as determined by the board of di rectors of the company. Issue at a Premium or a Discount The market price of stock is in uenced by many factors, such as: 1. Potential earning power. 2. General business conditions and other prospects. 3. Financial condition and earnings record. 4. Dividend record. Stock will be sold at a price above par if investors are willing to pay the excess, or premium. The premium is not pro t to the corporation but



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Fig. 8-5

(a) Since tan 40 Since cos 40 (b) Since tan 50 Since sin 40 (c) Since sin 40 Since cos 40 x 150(0.8391) 126. , x 150 tan 40 150 150 150 150 196. y ,y 0.766 cos 40 x , x 150 tan 50 150(1.1918) 179. 150 150 150 150 233. y ,y 0.6428 sin 40 x , x 150 sin 40 150 (0.6428) 96. 150 y , y 150 cos 40 150(0.776) 115. 150





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Solving trigonometry problems (a) An aviator flew 70 mi east from A to C. From C, he flew 100 mi north to B. Find the measure of the angle of the turn (to the nearest degree) that must be made at B to return to A. (b) A road is to be constructed so that it will rise 105 ft for each 1000 ft of horizontal distance. Find the measure of the angle of rise to the nearest degree, and the length of road to the nearest foot for each 1000 ft of horizontal distance.

(a) The required angle is m EBA 180 35 70 EBA in Fig. 8-6(a). In rt. nABC, tan B 0.7000; hence, m B 100 145 . 105 (b) We need to find m A and x in Fig. 8-6(b). Since tan A 0.1050, m A 6 . Then cos 6 1000 1000 1000 so x 1006 ft. 0.9945 cos 6 35 and 1000 x ,

Fig. 8-6

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Here are some definitions that are involved in observed-angle problems: The line of sight is the line from the eye of the observer to the object sighted. A horizontal line is a line that is parallel to the surface of water. An angle of elevation (or depression) is an angle formed by a horizontal line and a line of sight above (or below) the horizontal line and in the same vertical plane. Thus in Fig. 8-7, the observer is sighting an airplane above the horizontal, and the angle formed by the horizontal and the line of sight is an angle of elevation. In sighting the car, the angle her line of sight makes with the horizontal is an angle of depression.

Fig. 8-7

rather part of the investment of the stockholders. If the purchaser will not pay par value, the corporation may issue stock at a price below par.

Using an angle of elevation (a) Sighting to the top of a building, Henry found the angle of elevation to measure 21 . The ground is level. The transit is 5 ft above the ground and 200 ft from the building. Find the height of the building to the nearest foot. (b) If the angle of elevation of the sun at a certain time measures 42 , find to the nearest foot the height of a tree whose shadow is 25 ft long.

x (a) If x is the height of the part of the building above the transit [Fig. 8-8(a)], then tan 21 and 200 x 200 tan 21 200(0.3839) 77 ft. Thus, the height of the building is h x 5 77 5 82 ft. h (b) If h is the height of the tree [Fig. 8-8(b)], then we have tan 42 and h 25 tan 42 25(0.9004) 25 23 ft.

Fig. 8-8

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