Question

If sinA = `2/3`, then value of cot A is ______.

Options

• `sqrt5/2`

• `3/2`

• `5/4`

• `2/3`

Answer 1

If sinA = `2/3`, then value of cot A is `underline(sqrt5/2)`

Explanation:

 sinA = `2/3`     ...(Given)

`(BC)/(AC) = 2/3`   `["Since," sin theta = P/H]`

BC = 2x and AC = 3x

Now, In ΔABC, By Pythagoras theorem

AC² = AB² + BC²

(3x)² = AB² + (2x)²

9x² = AB² + 4x²

AB² = 9x² − 4x²

AB² = 5x²

AB = `sqrt5x`

`cot A = (AB)/(BC)`     ...`["Since", cot theta = B/P]`

= `(sqrt5x)/(2x)`

= `sqrt5/2`