Is there any possible way for me to obtain the length of the side of a right triangle if i only know the angles measures (90,60,30)

Question

I have a right triangle, but i only have the measures for its angles (90,60,30) Is there any way for me to find the length of one side

Answer 1

As Carol explained in her answer, if all you know is the 3 angles, then all you can get from that is the relative proportions of the 3 sides, so you can express any 2 sides in terms of the 3rd side.  Think of it as a matter of scale.  Draw a 30-60-90 triangle, and then redraw it twice as large.  The 2 triangles are both 30-60-90, but the sides have different lengths.  There are infinitely many lengths possible in a 30-60-90 triangle.  But if you know any one side, then you can get the other two using Pythagoras' theorem or trigonometry.

Answer 2

In a 30-60-90 right triangle, shorter side/hypotenuse = 1/2

longer side/hypotenuse = (√3)/2

Shorter side:longer side:hypotenuse = 1:√3:2

All multiples of that ratio will give you possible lengths of the three sides. For example, 2:2√3:4, etc.