The value of 'x' with rational denominator =
[tex] \frac{4 \sqrt{3} }{3} [/tex]
Step-by-step explanation:
cos =
[tex] \frac{adjacent \: side}{hypotenuse} [/tex]
cos 30 =
[tex] \frac{ \sqrt{3} }{2} [/tex]
given triangle is a right- angled triangle.
from the triangle,
cost 30 =
[tex] \frac{adjacent \: side}{hypotenuse} \: \: = \: \frac{2}{x} [/tex]
[tex] \frac{ \sqrt{3} }{2} \: = \frac{2}{x} [/tex]
√3x = 4
[tex]x \: = \: \frac{4}{ \sqrt{3} } [/tex]
Rationalising the denominator we get,
x =
[tex] \frac{4}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } [/tex]
x =
[tex] \frac{4 \sqrt{3} }{3} [/tex]
Therefore, the value of 'x' =
[tex] \frac{4 \sqrt{3} }{3} [/tex]
