Question

How do i do this it’s geometry

Answer 1

Answer:

Therefore the length of side x in simplest radical form with a rational denominator is

$x=2\sqrt{6}$

Step-by-step explanation:

Given:

Consider right triangle ABC

∠A = 60°

∠B = 90°

∠C = 30°

$AB=\sqrt{8}$

To Find:

BC = x = ?

Solution:

In Right Angle Triangle ABC Tan Identity

$\tan C= \frac{\textrm{side opposite to angle C}}{\textrm{side adjacent to angle C}}$

Substituting the values we get

$\tan 30 = \dfrac{AB}{BC}$

$\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{8}}{x}\\\\x=\sqrt{3}\times \sqrt{8}=\sqrt{24}=2\sqrt{6}$

Therefore the length of side x in simplest radical form with a rational denominator is

$x=2\sqrt{6}$