Plane and spherical trigonometry Volume 1 - Tapa blanda

Sinopsis

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1873 Excerpt: ...W.N.W. 49. (Fig. 47.) A ship S was 2640 yards due south of a lighthouse AB, and after sailing N.W.b.N. 800 yards to J), its angle of elevation BDA was 5 25'; required its height. Ans. 192 yards. 50. (Fig. 48.) The bearings of two objects A and B in the same latitude from a ship at C are N.N.E. and N.E.b.E., and the distance from A is 10 miles; required the distance from B. Ans. 16-63 miles. 51. (Fig. 49.) Find the angle which the line of metal makes with the axis produced in a piece whose dimensions are as follows: diameter of breach=12-44 inches; of muzzle =9-84 inches; length of gun=77£ inches. Ans. 0 57' 51". Calculations of a front of Fortification. 52, (Fig. 50.) Let AB be the exterior side of a regular pentagon, and suppose the side to be 350 yards, the perpendicular DE 50 yards, the face AH of the bastion 100 yards, and the line of defence AG equal to AK. As the length and position of the other lines depend on these values, it is required to find the magnitude and position of the following The following problems are given as exercises in analytical trigonometry and algebra. 53a. What angle will a tower subtend at a place whose distance is equal to six times its height 1 and where must an observer station himself that the angle of elevation may be double of the former? Ans. 9 28-; 2-9 times the height. 54a. (Fig. 51.) A maypole was broken by the wind, and its top struck the ground 20 feet from its base; and being again fixed was broken a second time 5 feet lower, and its top extended 10 feet farther; required its height. Ans. 50 ft. 55a. (Fig. 52.) The summit A of a hill bore due east of a spectator at B, and E.N.E. of a spectator at a point C due south of B; the elevation of the point A at B was 20; required its elevation at C. Ans. 18 36'....

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