Question

Find x. \/3 1.5 3 \/3 2

Answer 1

Answer:

x = $\sqrt{3}$

Step-by-step explanation:

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

tan60° = $\sqrt{3}$ , then

tan60° = $\frac{opposite}{adjacent}$ = $\frac{3}{x}$ = $\sqrt{3}$ ( multiply both sides by x )

3 = x × $\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

$\frac{3}{\sqrt{3} }$ = x , then rationalising the denominator

x = $\frac{3}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ = $\frac{3\sqrt{3} }{3}$ = $\sqrt{3}$

Answer 2

$x = \sqrt{3}$

Step-by-step explanation:

Given:

$\sin(ABC) = \frac{AC}{AB}$

$= > \sin(60) = \frac{3}{AB}$

$= >AB= 2 \sqrt{3}$

Now by Pythagoras theorem,

$AC^{2} + BC^{2} = AB^{2}$

Substituting values,

${3}^{2} + {x}^{2} = (2 \sqrt{3})^{2}$

$= > {x} = \sqrt{3}$

Hence, value of x is $\sqrt{3}$