Answer:
Therefore the length of side x in simplest radical form with a rational denominator is
[tex]x=2\sqrt{6}[/tex]
Step-by-step explanation:
Given:
Consider right triangle ABC
∠A = 60°
∠B = 90°
∠C = 30°
[tex]AB=\sqrt{8}[/tex]
To Find:
BC = x = ?
Solution:
In Right Angle Triangle ABC Tan Identity
[tex]\tan C= \frac{\textrm{side opposite to angle C}}{\textrm{side adjacent to angle C}}[/tex]
Substituting the values we get
[tex]\tan 30 = \dfrac{AB}{BC}[/tex]
[tex]\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{8}}{x}\\\\x=\sqrt{3}\times \sqrt{8}=\sqrt{24}=2\sqrt{6}[/tex]
Therefore the length of side x in simplest radical form with a rational denominator is
[tex]x=2\sqrt{6}[/tex]
