Question

Find the length of side x in simplest radical form with a rational denominator.

Answer 1

Answer:

x = (4√3)/3 units

Step-by-step explanation:

Here we have a right 60,30 Triangle with Side 2 units and Htpotenuse x units.

Now,

Sin 60° = Opp./Hyp

Sin 60° = 2/x

But we know that,

Sin 60° = √3/2

So,

√3/2 = 2/x

Cross multiplying we get,

x√3 = 4

x = 4/√3

Rationalizing the denominator,

x = (4/√3) × (√3/√3)

x = (4√3)/3 units

Hope it helped and believing you understood it........All the

Answer 2

Answer:

The value of 'x' with rational denominator =  $\frac{4\sqrt{3} }{3}$

Step-by-step explanation:

Recall the formula,

cos $\theta$ =  $\frac{adjascent \ side }{hypotenuse}$

cos 30 = $\frac{\sqrt{3} }{2}$

Given triangle is a right-angled triangle.

From the triangle,

cost 30 = $\frac{adjascent \ side }{hypotenuse}$ =  $\frac{2}{x}$

$\frac{\sqrt{3} }{2}$ =  $\frac{2}{x}$

√3x = 4

x = $\frac{4}{\sqrt{3} }$

Rationalising the denominator, we get

x = $\frac{4}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3}}$

x = $\frac{4\sqrt{3} }{3}$

∴ The value of 'x' with rational denominator =  $\frac{4\sqrt{3} }{3}$

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