If the acute angles of a right angled triangle have measures 30ᵒ and 60ᵒ then the length of the side opposite to 60ᵒ angles is √

× hypotenuse

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;

= +

= +

4 = + 1

= 4 - 1

   = 3

⇒ x =

The length of the side opposite 60ᵒ angle is units.

7

step-by-step explanation:

the answer would be 7