Measurement, STD2 EQ-Bank 13 MC

City A is at latitude \( 27^{\circ}\text{S} \) and longitude \( 153^{\circ}\text{E} \). City B is \( 45^{\circ} \) north of City A and \( 38^{\circ} \) east of City A.

What are the latitude and longitude of City B?

\( 18^{\circ}\text{N} \), \( 191^{\circ}\text{E} \)
\( 18^{\circ}\text{N} \), \( 115^{\circ}\text{E} \)
\( 72^{\circ}\text{S} \), \( 191^{\circ}\text{E} \)
\( 18^{\circ}\text{N} \), \( 169^{\circ}\text{W} \)

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\(D\)

Show Worked Solution

\(\text{Latitude of City B}=45^{\circ}-27^{\circ}=18^{\circ}\text{N}\)

\(\text{Longitude of City B}=153^{\circ}+38^{\circ}=191^{\circ}\text{E}\)

\(\text{Since longitude}\ \gt 180^{\circ},\ \text{convert to Western hemisphere:\)

\(191^{\circ}-180^{\circ}=11^{\circ}\)

\(\text{Longitude}\ = 180-11=169^{\circ}\text{W}\)

\(\Rightarrow D\)