Find the angle between the two forces acting on the particle, F1=60N, F2=80N and the resultant force=100N

please explain

thank you

As Chandler said, the two forces and their resultant satisfy:
[F(1)]^2 + [F(2)]^2 = [F(resultant)]^2,

so if draw out the two forces and their resultant, the resulting triangle will be a right triangle (since their sides satisfy the Pythagorean Theorem) with the 90° in-between the two sides that the two forces make. Hence, the angle between the two force vectors is 90°.

In general, to find the angle between the two vectors, you will need to use the Law of Cosines. If we call c the resultant, then C is the angle between the two force vectors (since the angle between the two force vectors is directly opposite to the resultant). By the Law of Cosines:
c^2 = a^2 + b^2 - 2ab*cos(C),

where a and b are the magnitude of the two force vectors, c is the magnitude of the resultant vector, and C is the angle between a and b.

I hope this helps!

The angle = 90 degrees, because

(60)^2 + (80)^2 = 3600 + 6400 = 10000 = (100)^2
(60)^2 + (80)^2 = (100)^2

The three forces form a right triangle.

tan = o/a = 60/80 = .6667

tan 34 = .6745

tan 35 = .7002

One must interpolate to find the exact angle.