VERTICAL DIALLING; OR, THE MENSURATION OF HEIGHTS. Rule.-Observe the given side and angle, and work by the respective cases as heretofore. From the bottom of a tower at B, I measured 200 feet in a direct line B A on an horizontal plane; I then took the angle A42° required the height of the tower and staff B C. In operations of this nature the hypothenuse need not be regarded. EXAMPLE II. Wanting to ascertain the height of an irregular hill, I proceed, from the several stations A, B, and C, to take the angles and measure the distances as follows, viz.: MISCELLANEOUS EXAMPLES IN THE FOREGOING RULES. Given the hypothenuse 14 feet 5 inches, angle 88': required the base and perpendicular.* Given the perpendicular 100 feet, angle 60°: required the hypothenuse and base. ft. in. AnswerB173 2-428 Given the base 118 feet, angle (Comp.) 23°: required the hypothenuse and perpendicular. Given the angle 53°: required the underlay in a fathom.† fath. ft. in. Answer 1 1 11-5472 Given the angle 36° 45': required the underlay in a fathom. ft. in. Answer 4 5:5650 Given the angle 4° 15′; required the underlay in a fathom. in. Answer 5-3496 A diagonal shaft having been sunk 8° 30′ out of its true course; what will be the extent of departure, supposing the length of the shaft 76 feet? ft. in. Answer 11 4.9577 Suppose a diagonal shaft was sunk as follows, viz: 2870 014 5 * In single drafts, one or two figures of the decimal will be sufficient, the others may be rejected. It has been before observed, that the underlay is given in the base of the second table. Required the sum of the bases and perpendiculars. Answer Bases 169 6-90784 Wanting to know the distance between two shafts, inaccessible in a right line, I measured from the first shaft 126 feet, on an angle of 27° 15′ E. by N.; from this station to the second. shaft the line measured 91 feet, on an angle of 42° 30′ N. by W.: how far are the shafts apart? ft. in. Answer 179 1.3 Wanting to know the altitude of a precipice, I measure off from its base 66 feet, and from thence I take the angle to the summit, which I find to be 42° (and consequently the complement 48°): required the height. ft. in. Answer 59 5-91999 At the foot of a hill the angle to the summit was 36°, from this place an adit had been driven in a direct line 218 feet: how far must I measure up the hill to put down a perpendicular shaft on the end of the adit, and what will be the depth of the shaft? At the foot of a diagonal shaft, 28 fathoms in length, sunk on a lode 27° 45′ underlaying north, another lode was cut making an angle 48° 45' underlaying south: what is the distance from the brace of the shaft to the back of the north lode? A perpendicular shaft having been sunk 168 feet in the side of a mountain, the slope or declivity making an angle with the shaft of 54° 15′ : required to know how far I must measure down the hill to get at the right spot for driving an adit to come in the exact depth of the shaft,-the length of the adit is also required. A lode underlaying south was observed to make an angle of 17° 15': required to know what distance from the back of the lode will be proper for sinking a perpendicular shaft that shall intersect the lode at the depth of 45 fathoms. |