Elements of geometry and trigonometry . E=41o 04 : in order to find BE, we shall liave to solvethe right angled triangle BCE, in which the angle C and theadjacent side CE are known. To find the side EB. As R - Is to tang. C 4r 04 So is EC To EB Hence, EB= yards. To EB add the height of theinstrument, which we will suppose to be yards, we shallthen have the required height AB= yards. If, in the same triangle BCE it were required to find thehypothenuse, form the proportionAs cos C 41- 04 - - log. IstoR
Elements of geometry and trigonometry . E=41o 04 : in order to find BE, we shall liave to solvethe right angled triangle BCE, in which the angle C and theadjacent side CE are known. To find the side EB. As R - Is to tang. C 4r 04 So is EC To EB Hence, EB= yards. To EB add the height of theinstrument, which we will suppose to be yards, we shallthen have the required height AB= yards. If, in the same triangle BCE it were required to find thehypothenuse, form the proportionAs cos C 41- 04 - - log. IstoR So is CE To CB : . - Note. If only the summit B of the building or place whoseheight is required were visible, we should (htermine the dis-tance CE by the method shown in the following example;this distance and the given angle BCE arc sufficient for solv-ing the riglit angled triangle BCE, whose side, increased bythe height of the instrument, will be the height required. 250 PLANE TRIGOTSJOMETRY. 2. To find upon the ground the distance of the point A ^ from an inaccessible object - ^-^^/i^ B, we must measure a base AD, and the two adjacent *^fe™ angles BAD, ADB. Sup- -^ pose we have found AD= yards, BAD = 103° 55 55,andBDA = 36°04; we shall thence get the third angle ABD=40° 05, and to P^^^—— ^^^ obtain AB, we shall form the proportion As sine ABD 40° 05 - log. - Is to sin BDA 36° 04 So is AD To AB - - [3 If for another inaccessible object C, we have found the an-gles CAD = 35° 15, ADC = 119° 32, we shall in like mannerfind the distance AC = yards. 3. To find the distance between two inaccessible objects Band C, we determine AB and AC as in the last example ; weshall, at the same time, have the included angle BAC=BAD—DAC. Suppose AB has been found equal to yards,AC = yards, and the angle BAC=:68° 40 55; toget BC, we must resolve th
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
