Step 1:
Draw the parallelogram
Step 2
Let the length of the shorter diagonal be L
Apply the cosine rule to find the length of the shorter diagonal L.
[tex]\begin{gathered} L^2=a^2+b^2\text{ - 2abcos58} \\ \text{a = 4 and b = 6} \end{gathered}[/tex]
Step 3:
Substitute in the formula
[tex]\begin{gathered} L^2=4^2+6^2-2\times4\times6\cos 58 \\ L^2\text{ = 16 + 36 - 48 }\times0.5299 \\ L^2=\text{ 52 - 25.4352} \\ L^2\text{ = 26.5648} \\ L\text{ = }\sqrt[]{26.5648} \\ L\text{ = 5.15} \\ L\text{ = 5.2 meters Option D} \end{gathered}[/tex]
Final answer
5.2 meters Option D
