Question

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​

Answer 1

`√(3)` units

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;

`/hyp/^(2)` =
`/adj1/^(2)` +
`/adj2/^(2)`

`/2/^(2)` =
`x^(2)` +
`/1/^(2)`

4 =
`x^(2)` + 1

`x^(2)` = 4 - 1

= 3

⇒ x =
`√(3)`

The length of the side opposite 60ᵒ angle is
`√(3)` units.