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If cos θ = 5/13, what is the value of tan θ&n...

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

E.

5/12

Correct answer is D

cosθ=513

In the right- angled triangle, with an angle θ, the adjacent side to θ = 5 and the hypotenuse = 13.

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

= 12.

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