The third problem of the Sea Island Manual goes as follows (see: Frank J. Swetz,

Question

The third problem of the Sea Island Manual goes as follows (see: Frank J. Swetz, The Sea Island Mathematical Manual (Pennsylvania State University Press, 1992), pp.21-22): Looking southward at a square walled city of unknown size, erect two poles 6 zhang apart in the east-west direction such that they are standing at eye level and are joined by a string. Assume that the eastern pole is aligned with the southeastern and northeastern comers of the city. Move northward 5 bu from the eastern pole and sight on the northwestern comer of the city; the line of observation intersects the string at a point. The side of the squared city measures 3 1i 43 3/4 bu. The city lies 4 li 45 bu from the pole. (For Your Information: 1 li = 1800 chi; 1 zhang = 10 chi; 1 bu = 6 chi; 1 chi = 10 cun) A drawing might help here. The two poles with the string in between are P and Q, with PQ = 6 zhang, R is the first point of measurement, S the second. We have PR = 5 bu, PT = 2 zhang 2 chi 6.5 cun, PS =13 bu 2 chi. a) Let EP = x and EF =y. Show how the in-out principle when applied to T in the rectangle defined by ERF and applied to Q in the rectangle defined by ESF, immediately leads to a system of linear equations in x and y. b) Solve the system and compare your answer with the answer above. c) Solve the problem using similar triangles.

Explanation / Answer

consider similar triangles

we see

that the trainagles are similar

so yhe equations become like this ou onsider

wo equation s

if y

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