. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. nowthe distance to a house, which stood on the other side, Imeasured 200 yards in a right line by the side of the riv-er, and found, that the two angles at each end of this line,formed by the other end and the house, were 73° 15, and68° 2. What was the distance between each station andthe house ? vr HEIGHTS AND DISTANCES. ill ZA 73° 15ZB 68 02 Sum 141 17From 180 00 ZC 38 43 9-7962062 ZA 73 15 9-9811711 AB 200 2-3010300 BC
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. nowthe distance to a house, which stood on the other side, Imeasured 200 yards in a right line by the side of the riv-er, and found, that the two angles at each end of this line,formed by the other end and the house, were 73° 15, and68° 2. What was the distance between each station andthe house ? vr HEIGHTS AND DISTANCES. ill ZA 73° 15ZB 68 02 Sum 141 17From 180 00 ZC 38 43 9-7962062 ZA 73 15 9-9811711 AB 200 2-3010300 BC 306-19 2-4859949 ZC 38° 43 9-7962062 ZB 68 02 9-9672679 AB 200 2-3010300 AC 296-54 2-4720917 Note. If in the right line ABa you measure Ba equalAB, and the line CBc be produced until the angle a beequal to the Angle A ; the distances Be, act will be equalto BC, AC. 112 MATHEMATICS. 2. Wanting to know the breadth of a river, I measured100 yards in a right line close by one side of it ; and ateach end of this line I found the angles, subtended by theother end and a tree close by the other side of the river*to be 53° and 79° 12. What is the perpendicular breadth ?. ZA 53° 00ZB 79 12 Sum 132 12From 180 00 ZATB 47 48ZB 79 12 AB 100 AT 9-869703?9*99223852*0000000 2-1225348 ZP 90° ZA 53 AT TP 105-89 10-00000009-90234862-1225348 2-0248834 HEIGHTS AND DISTANCES. 115 3. Two ships of war, intending to cannonade a fort, are,by the shallowness of the water, kept so far from i ,that they suspect their guns cannot reach it ; in ordertherefore to measure the distance, they separate from eachother half a mile, or 880 yards ; then each ship observesthe angle, which the other and the fort subtend, and theyare found to be 85° 15 and 83° 45. What is the distancebetween each ship and the fort ? faSar ZA 83° 45 ZB 85 15 « Sum 169 00 From 180 00 ZF 11 00 9*2805988 ZA 83 45 9-9974110 AB 880 2-9444827 BF 4584-5 3-6612949 ZF^ 11° 00 9-2805988 ZB 85 15 9-9985058 AB 880 2-9444827 AF 45961 3-6
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