Question

The sides of a parallelogram are 4 meters and 6 meters. One angle is 58° while another is 122°. Find the length of the shorter diagonal.

Answer 1

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.

`\begin{gathered} L^2=a^2+b^2\text{ - 2abcos58} \\ \text{a = 4 and b = 6} \end{gathered}`

Step 3:

Substitute in the formula

`\begin{gathered} L^2=4^2+6^2-2*4*6\cos 58 \\ L^2\text{ = 16 + 36 - 48 }*0.5299 \\ 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}`

Final answer

5.2 meters Option D