Problema Solution
Determine the lengths of the diagonals, perimeter and area of the parallelogram if one of the angles of the parallelogram is 27 degree and 15 minutes with sides measuring 180 meters and 70 meters.
Answer provided by our tutors
First the perimeter:
The shape is a parallelogram, and therefore by definition has two pairs of sides of equal length. Therefore the perimeter is 2*180+2*70=500 meters
Next the Diagonals:
This requires the law of cosines (C^2=A^2+B^2-2*A*B*cos(c))
C is the diagonal and the other two sides are A and B. The angle given is c. From there it is just plug and chug to get C is about 224.5. Repeat with the same A and B, but this time use the supplment of the angle (180 minus 27.25). This results in 216.1.
Area:
This is base times height. I used the base as 70 meters and the height as 180*sin(27.25). Therefore, the area is 10765 meters squared.