Answer:
[tex]\sqrt{3}[/tex] units
Step-by-step explanation:
Considering an equilateral triangle, the measure of the angles are 60ᵒ each and the sides have equal length of 2 units. If the equilateral triangle is divided into two equal right triangles, we have angles 30ᵒ, 60ᵒ and a right angle.
Let the value of the side opposite 60ᵒ angle be represented by x., the side opposite the right angle is 2 units, and that opposite the 30ᵒ is 1 unit.
Applying the Pythagoras theorem to determine the unknown side of the triangle, we have;
[tex]/hyp/^{2}[/tex] = [tex]/adj1/^{2}[/tex] + [tex]/adj2/^{2}[/tex]
[tex]/2/^{2}[/tex] = [tex]x^{2}[/tex] + [tex]/1/^{2}[/tex]
4 = [tex]x^{2}[/tex] + 1
[tex]x^{2}[/tex] = 4 - 1
= 3
⇒ x = [tex]\sqrt{3}[/tex]
The length of the side opposite 60ᵒ angle is [tex]\sqrt{3}[/tex] units.
