SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Explain the formula to use
Using the cosine rule which states that:
[tex]z^2=x^2+y^2-2xy\cos Z[/tex]
STEP 2: Write the given sides
[tex]x=4,y=6,Z=41^{\circ},z=?[/tex]
STEP 3: Find the value of z
[tex]\begin{gathered} By\text{ substitution,} \\ z^2=4^2+6^2-2(4)(6)\cos41 \\ z^2=16+36-48cos41 \\ z^2=52-36.22605985 \\ z^2=15.77394015 \\ z=\sqrt{15.77394015} \\ z=3.971641997 \\ z\approx4.0 \end{gathered}[/tex]
Hence, the indicated length is 4.0
