If cos θ = 5/13, what is the value of tan \(\theta\) for 0 < θ < 90° ?

  • A 13
  • B 5
  • C 13/5
  • D 12/5
  • E 5/12
waec 1992mathematics

The correct answer is D. 12/5

\(\cos \theta = \frac{5}{13}\)

\(\implies\) In the right- angled triangle, with an angle \(\theta\), the adjacent side to \(\theta\) = 5 and the hypotenuse = 13.

\(\therefore 13^2 = opp^2 + 5^2\)

\(opp^2 = 169 - 25 = 144 \implies opp = \sqrt{144}\)

= 12.

\(\tan \theta = \frac{opp}{adj} = \frac{12}{5}\)

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