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Convert the quadrantal bearing N45° 30' 25" W to a Whole Circle Bearing (WCB).

Mathematics

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Answer

314∘ 29’ 35”\text{314}^\circ \text{ 29' 35''}

Step-by-step solution

2 steps

  1. Interpret the given bearing.

    The bearing is given as N45° 30' 25" W. This is a quadrantal bearing. It indicates that the line is in the Northwest quadrant, meaning the angle is measured 45 degrees, 30 minutes, and 25 seconds from the North meridian towards the West.

  2. Convert to Whole Circle Bearing (WCB).

    Whole Circle Bearing (WCB) is measured clockwise from the North meridian, ranging from 0° to 360°.
    For a line in the Northwest quadrant (N α\alpha W), the WCB is calculated as 360∘−α360^\circ - \alpha.

    In this case, α=45∘30′25′′\alpha = 45^\circ 30' 25''.

    WCB=360∘−45∘30′25′′\text{WCB} = 360^\circ - 45^\circ 30' 25''

    To perform the subtraction, we can rewrite 360∘360^\circ as 359∘59′60′′359^\circ 59' 60'':

    WCB=359∘59′60′′−45∘30′25′′=(359−45)∘(59−30)′(60−25)′′=314∘29′35′′\begin{align*} \text{WCB} &= 359^\circ 59' 60'' - 45^\circ 30' 25'' \\ &= (359 - 45)^\circ (59 - 30)' (60 - 25)'' \\ &= 314^\circ 29' 35'' \end{align*}

    The equivalent whole circle bearing of the line is:

    314∘ 29’ 35”\text{314}^\circ \text{ 29' 35''}
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