Question

If cos θ = 4/5,  then find the value of tan θ.

Answer 1

Let,

Base =BC = 4k

Hypotenuse =AC = 5k

Where, k ia any positive integer

So, by Pythagoras theorem, we can find the third side of a triangle

⇒ (AB)² + (BC)² = (AC)²

⇒ (AB)² + (4k)² = (5k)²

⇒ (AB)² + 16k² = 25k²

⇒ (AB)² = 25 k² –16 k²

⇒ (AB)² = 9 k²

⇒ AB =√9 k²

⇒ AB =±3k

But side AB can’t be negative. So, AB = 3k

Now, we have to find tan θ

We know that,