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10 August, 11:53

A water main is to be constructed with a 20 % grade in the north direction and a 25 % grade in the east direction. determine the angle theta required in the water main for the turn from north to east.

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  1. 10 August, 14:21
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    Let n = North

    and e = east

    using vectors,

    n = j + 0.20 k

    e = i + 0.25 k

    n · e = 1x0 + 0x1 + 0.20*0.25 = 0.05

    |n|·|e| = i (1² + 0.20²) ·i (1²+0.25²) = 1.105

    E° = arccos ((n · e) / |n|·|e|)

    E° = arccos (0.05/1.105)

    E° = arccos (0.0452)

    E° = 87.40°
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