Question

Evaluate sin 60° without using a calculator by using ratios in a reference triangle. I don't understand. Do I explain how the sides are rationed or what?

Answer 1

The drawing shows an equilateral triangle, with each of the three sides having a length of 2 units. The line from the vertex bisects the horizontal side, making two triangles each triangle having a right angle. By the theorem of Pythagoras the length of the vertical line is the square root of 3.
You can now use the formula
\[\sin 60\ degrees=\frac{length\ of \ opposite\ side}{length\ of\ hypotenuse}\]
to get the required ratio.