Question

Help????? I don’t know which is right

Answer 1

C

Explanation:

Given

tanθ =
`(1)/(2)` =
`(opposite)/(adjacent)`

This is a right triangle with legs 1 and 2

Using Pythagoras' identity

hypotenuse² = 1² + 2² = 1 + 4 = 5 ( take square root of both sides )

hypotenuse =
`√(5)`

θ is in the 3rd quadrant where sinθ < 0 , then

sinθ =
`(opposite)/(hypotenuse)` = -
`(1)/(√(5) )` ← rationalise the denominator

= -
`(1)/(√(5) )` ×
`(√(5) )/(√(5) )`

= -
`(√(5) )/(5)` → C