Question

If `sin θ = 5/13`, then the value of tan θ is ______.

Answer 1

If `sin θ = 5/13`, then the value of tan θ is `underlinebb(5/12)`.

Explanation:

Given, `sin θ = "Opposite side"/"Hypotenuse"`

Using Pythagoras theorem,

x² + (5k)² = (13k)²

⇒ x² = 169k² – 25k²

⇒ x² = 144k²

⇒ x = 12k   ...[Where k ≠ 0]

Hence, tan θ = `"Opposite side"/x`

= `(5k)/(12k)`

∴ `tan θ = 5/12`