If cos θ = 5/13, what is the value of tan \(\theta\) for 0 < θ < 90° ?
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Correct Answer: Option D
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.
\(\tan \theta = \frac{opp}{adj} = \frac{12}{5}\)
\(\cos \theta = \frac{5}{13}\)
\(\implies\) 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.
\(\tan \theta = \frac{opp}{adj} = \frac{12}{5}\)