Question

If sin θ = `1/9`, then tan θ is equal to ______.

Options

• `1/(4sqrt(5))`

• `(4sqrt(5))/9` 

• `1/8`

• `4sqrt(5)`

Answer 1

If sin θ = `1/9`, then tan θ is equal to `underlinebb(1/(4sqrt(5)))`.

Explanation:

sin θ = `1/9 = P/H`

ABC is right-angled.

AB² = BC² + AC²

(9K)² = BC² + K²

81K² – K² = BC²

80K² = BC²

BC = `sqrt(80K^2)`

BC = `4sqrt(5)K`

tan θ = `P/B`

tan θ = `(AC)/(BC)`

tan θ = `K/(4sqrt(5)K)`

tan θ = `1/(4sqrt(5))`