Finding Magnitude of Two Forces

Hi shama, let's solve this together. We need to find the magnitudes of two forces acting at a point given their relative magnitude, the angle between them, and the magnitude of their resultant force.

Let's represent the magnitude of the smaller force as F sub one, and the larger force as F sub two.

Since the magnitude of one force is five over two times the other, we can write F sub two as two point five times F sub one.

Now, let's recall the formula for the magnitude of the resultant of two forces acting at an angle theta.

Let's substitute F sub two equals two point five times F sub one into our formula.

We can simplify this by squaring two point five and multiplying two by two point five.

Now, let's factor out F sub one squared from all the terms on the right-hand side.

Next, let's calculate the numerical terms inside the parentheses. We start with the value of cosine fifty-five degrees.