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Points P and Q are respectively 24m north and 7m east of point R. What is...

Mathematics
WAEC 1988

Points P and Q are respectively 24m north and 7m east of point R. What is the bearing of Q from P to the nearest whole degree?

  • A. 16o
  • B. 17o
  • C. 73o
  • D. 106o
  • E. 164o
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Correct Answer: Option E
Explanation

Using Pythagoras' theorem:

Hyp\(^2\) = Adj\(^2\) + Opp\(^2\) → 24\(^2\) + 7\(^2\)

Hyp = \(\sqrt{625}\) → 25

\(\tan P = \frac{7}{24}\)

tan P = 0.2917

P = tan\(^{-1}\) (0.2917)

= 16.26° 

Bearing of Q from P = 180° - 16.26°

= 163.74° \(\approxeq\) 164°


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