畢氏定理(難)

圖片參考：http://juniormaths.learnmore.com.hk/OUP/JMaths/Paper/images/lm2b13_paper1b_q002.jpg

設XZ=5x cm ,YZ=8x cm
(XY)^2+(XZ)^2=(YZ)^2 [畢氏定理]
(34)^2+(5x)^2=(8x)^2
1156+25x^2=64x^2
39x^2=1156
x=5.44
所以,YZ=8(5.44)=43.6cm(準至三位有效數字)

XY:XZ:YZ = (8^2-5^2)^0.5 : 5 : 8 = 6.245 : 5 : 8

Therefore YZ = 34 x 8/6.245 = 45.6 cm

先求 XZ， 然後再用畢氏定理求YZ。
XZ : YZ = 5:8
XZ / YZ = 5/8
XZ = (5/8) * YZ

XY^2 + XZ^2 = YZ^2
(34)^2 + ((5/8) * YZ)^2 = YZ^2
1156 = YZ^2 - (0.390625 * YZ^2)
1156 = 0.609375 * YZ^2
1897.025641 = YZ^2
YZ = 43.5548578 or 43.6 (3 sig. fig)