Problems in the Different Branches of Philosophy; Adapted to the Course of Reading Pursued in the University of Cambridge - Softcover

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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. 1830. Excerpt: ... jects on the horizontal plane which are in the same straight line with the tower, to be 30 and 45. Determine their distance from each other and from the observer. 9. From the top of a tower, whose height is 108 feet, the angles of depression of the top and bottom of a vertical column standing in the horizontal plane, are found to be 30 and 60 respectively. Determine the height of the column. 10. From the top and bottom of a building whose height is known, the elevation of another building on the same horizontal plane is observed; shew how the height and distance of the second building may be determined from these observations: and find that point in the plane which is equidistant from the top of each: also the point where the angles of elevation of the two buildings are equal. 11. Two observers, stationed at the distance of a quarter of a mile from each other, observed the altitude and bearing of a balloon at the same instant of time. One of them found its altitude a0, and bearing N. N. W., and the other b, and bearing N. W. Determine the perpendicular height of the balloon. 12. The altitude of a cloud was observed to be a", and that of the sun in the same direction b; and the distance of the shadow of the cloud from the station of the observer measured c yards. Determine the height of the cloud. 13. Having at a certain (unknown) distance taken the angle of elevation of a steeple, I advanced 60 yards nearer on level ground, and then observed the angle of elevation to be the complement of the former. Advancing 20 yards still nearer, the angle of elevation now appeared to be just double of the first. Determine the altitude of the steeple. 14. Having given the hypothenuse--a, and the sum of the two sides of a right-angled triangle =b; find the sides and angl...

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