Question

ABC is a right angled triangle, right angled at C. D is the midpoint of BC. Then, \(\frac{\tan \theta}{\tan \phi} \) =

(a) 1

(b) \(\frac 1{\sqrt 2}\)

(c) \(\frac 12\)

(d) 2

Answer 1

Correct option is (c) \(\frac 12\)

\(\frac{\tan \theta}{\tan \phi } = \cfrac{\frac{AC}{BC}}{\frac{AC}{DC}}\)

\(= \frac {DC}{BC}\)

\(= \frac {DC}{2DC}\)

\(= \frac 12\)   (Since, BC = 2DC, D being the mid point of BC)