Question

If cosθ = 4/5  then tan θ = ? 

(a) 3/4 

(b) 4/3 

(c) 3/5 

(d) 5/3

Answer 1

Correct answer is (a) 3/4

Since cos θ = 4/5 but cos θ = AB/AC 

So AB/AC = 4/5 

Thus, AB = 4k and AC = 5k

Using Pythagoras theorem in triangle ABC, we have: 

AC² = AB² + BC² 

⇒ BC² = AC² − AB² 

⇒ BC² = (5k)² − (4k)² 

⇒ BC² = 9k² 

⇒ BC = 3k 

∴ tan θ = BC/AB = 3/4