If cos θ = 5/13, what is the value of tan θ for 0 <
MATHEMATICS
WAEC 1992
If cos θ = 5/13, what is the value of tan θ for 0< θ< 90° ?
- A. 13
- B. 5
- C. 13/5
- D. 12/5
Correct Answer: D. 12/5
Explanation
\(\cos \theta = \frac{5}{13}\)
\(\implies\) 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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