As in Example 9, assume that the carpenter’s diagonal measurements are x and y, and compute the diagonal length that produces a rectangular frame. Compare the result with the corresponding split-difference approximation.

x = 87.2 cm and y = 82.7 cm

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EXAMPLE 9 Let us return to the problem posed at the start of the section (see Figure 13). We have a wind vector w = (60,0) km/h, and the bridge is oriented 32 degrees east of north. Express w as a sum of vectors, one parallel to the bridge and one perpendicular to it. Also, compute the magnitude of the vector perpendicular to the bridge to determine the speed of the part of the wind blowing directly at the bridge. 32°/u 58°