In triangle EFG, given e= 4 units, E = 43 deg and G= 54 deg, find f.

To find the length of side 'f' in triangle EFG, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle.

Here are the steps to solve for 'f':

1. First, we need to find the measure of angle 'F'. Since the sum of the angles in a triangle is 180 degrees, we subtract the given angles from 180.

   F = 180 - E - G F = 180 - 43 - 54 F = 83 degrees

2. Now, we can use the Law of Sines to find 'f'. We set up the equation as follows:

   e/sin(E) = f/sin(F)

3. Substitute the given values into the equation:

   4/sin(43) = f/sin(83)

4. Solve for 'f':

   f = (4/sin(43)) * sin(83)

5. Calculate the value:

   f ≈ 6.37 units

So, the length of side 'f' in triangle EFG is approximately 6.37 units.