Mathematical Exercises

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1877 edition. Excerpt: ...the mountain. 28. From the top of a tower, whose height is 108 ft., the angles of depression of the top and bottom of a vertical column standing on the horizontal plane are 30 and 60 respectively. Find the height of the column. 29. From each of two ships a mile apart the angle which is subtended by the other ship and the beacon on shore is observed; these angles are 55 and 62 30'. Determine the distances of the ships from the beacon. 30. Four trees, A, B, C, D, are in the same straight line. The distance AB=40 yards, BC=20 yards, CD=60 yards. P is a point, out of the line, such that the distances between the trees appear equal to each other. Find AP, BP, CP, DP. 31. The angle between a fort and a lighthouse observed from a ship at sea is 56 30', but after the ship has sailed half a mile in the direction of the fort, the angle between the same two objects is 70 45'. What was the ship's distance from the lighthouse midway between the two places of observation? 32. The distance from A to B is l-75 mile, from B to C 25 miles, and these three stations are in the same straight line. I travel, not in that straight line, from C to a station D, and then observe that the stations B and C subtend at my eye an angle of 23 19', and A and B an angle of 17 49'. Find the distances of D from A and B. 33. The boundary of a breakwater seen from either A or B, two stations 1250 yards apart (of which A is due south of one extremity, B due east of the other), subtends an angle of 15. Find the rectilineal distance between the ends of the breakwater. 34. At what distance may a light, which is 60 ft above the level of the sea, be just seen from the deck of a ship 12 ft. above the level of the sea, the earth being considered a sphere of 4000 miles radius?, 35. At...