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
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})