Using a scale of 1 cm to represent 10 N, find the size and

direction of the resultant of forces of 30 N and 40 N acting

at right angles to each other?

The size of the resultant is given by using pythagoras:

C^2 = A^2 + B^2

Since the 30N force and the 40N force act perpendicular to one another.

So: C = sqrt[ (30) ^2 + (40) ^2]

C = 50N and, therefore, may be represented using 5cm

Since all we have as reference are the 2 initially given forces, let's use the angle between the resultant force and one of them to determine the resultants direction:

Taking the 40N force as a baseline (you can imagine it being horizontal).

Since the 40N force is a horizontal projection of the 50N resultant force:

40N = 50N*cos (theta); where theta is the angle formed between them

Theta is approximately 36,87° and that is the direction of the resultant force taken with the 40N forces direction as reference.

You can also graphically establish this direction by simply drawing the lines in scale on a piece of paper.