of course you can.  However, to draw the exact triangle, you would need one of the side lengths, but you can draw the shape itself at an arbitrary scale without it. Why/how/?  Sine and cosine are ratios.  Whichever one you know, it forces you to have two of the three sides of the triangle, and if you know two sides and an angle, you define a triangle, no matter what.

Your example is an easy one, because you have a right triangle and define the hypotenuse as 5 and the opposite side from the angle as 4 (sine=opposite/hypotenuse=4/5).  Well, that forces a right-3-4-5 triangle (tells you that the third side is length of 3).

:-

sin ∅ = 4/5

cos ∅ = 3/5

tan ∅ = 4/3

Can then draw right angled triangle with sides in ratio of 3 : 4 : 5

Such a right angled triangle could have sides 6 cm , 8 cm and 10 cm

It only helps if the angle one of the acute angles of a right triangle.  That's what the "SOH CAH TOA" ratio definitions are based on.

If that's the case (trig ratio value given for an acute angle of a right triangle) then the ratio value determines the exact shape of the right triangle.  You can use that one value to construct a triangle that's geometrically similar to the original.

Suppos you're given that example, where the sine one angle is 4/5.  Let that be angle A, and label the other acute angle as B and the right angle as C. Then label the sides opposite A, B, C as a, b, c respectively.  That's the usual setup, right?

So, you need sin A = a/c to be 4/5.  An easy way to to that is to let a=4 and c=5.  Pythagoras tells you that:

    b = √(c² - a²) = √(5² - 4²) = √(25 - 16) = √9 = 3.

Now you can sketch a right triangle with legs of 3 units and 4 units; and every right triangle with an angle A such that sin A = 4/5 will be that same shape.

You know that one angle is a right angle and you know that one of the other angles has a sine value of 4/5.  Since you have 2 of the angles, you'll automatically have the 3rd angle.  Can you draw the exact triangle?  No, because you don't have a single side length.  However, you can draw an accurate scaled version of the triangle.

If you know it's a right triangle and you know the sine of one angle is 4/5, then you can sketch the triangle.  It won't be to scale as you won't know the exact length.

The sine of a right triangle is defined as the opposite over the hypotenuse.  So knowing the sine is 4/5, then we know the opposite of the angle is 4 and the hypotenuse is 5.  Solving for the unknown adjacent length we get:

a² + b² = c²

4² + b² = 5²

16 + b² = 25

b² = 9

b = 3

So we know that the lengths are in a ratio of 3:4:5.  If the lengths are 3, 4, 5 or 30, 40, 50, or 300, 400, 500.  They still will look the same, just larger.

No I couldn't.  Artistic ability aside, I could only get the proportions of the triangle from that information.  There's no way of knowing whether the actual opposite side and hypotenuse are 4 and 5, or .004 and .005