Question

Find x.



\/3
1.5
3 \/3
2

Answer 1

x =
`√(3)`

Explanation:

Using the tangent ratio in the right triangle and the exact value

tan60° =
`√(3)` , then

tan60° =
`(opposite)/(adjacent)` =
`(3)/(x)` =
`√(3)` ( multiply both sides by x )

3 = x ×
`√(3)` ( divide both sides by
`√(3)` )

`(3)/(√(3) )` = x , then rationalising the denominator

x =
`(3)/(√(3) )` ×
`(√(3) )/(√(3) )` =
`(3√(3) )/(3)` =
`√(3)`

Answer 2

`x = √(3)`

Explanation:

Given:

`\sin(ABC) = (AC)/(AB)`

`= > \sin(60) = (3)/(AB)`

`= >AB= 2 √(3)`

Now by Pythagoras theorem,

`AC^(2) + BC^(2) = AB^(2)`

Substituting values,

`{3}^(2) + {x}^(2) = (2 √(3))^(2)`

`= > {x} = √(3)`

Hence, value of x is
`√(3)`