Question

How do i do this it’s geometry

Answer 1

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

`x=2√(6)`

Explanation:

Given:

Consider right triangle ABC

∠A = 60°

∠B = 90°

∠C = 30°

`AB=√(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 = (AB)/(BC)`

`(1)/(√(3))=(√(8))/(x)\\\\x=√(3)* √(8)=√(24)=2√(6)`

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

`x=2√(6)`