Answer:
[tex]Area = 2288.754m^2[/tex]
Step-by-step explanation:
The given parameters can be represented as:
[tex]A = 52m[/tex]
[tex]B=90m[/tex]
[tex]\theta = 102^{\circ}[/tex]
Required
Determine the area of the garden
Provided that [tex]\theta[/tex] is between A and B, the area is:
[tex]Area = \frac{1}{2}AB sin(\theta)[/tex]
Substitute values for A, B and [tex]\theta[/tex]
[tex]Area = \frac{1}{2}AB sin(\theta)[/tex]
[tex]Area = \frac{1}{2} * 52 * 90 * sin(102)[/tex]
[tex]Area = \frac{1}{2} * 52 * 90 * 0.9781[/tex]
[tex]Area = \frac{52 * 90 * 0.9781}{2}[/tex]
[tex]Area = \frac{4577.508}{2}[/tex]
[tex]Area = 2288.754[/tex]
Hence, the area of the garden is [tex]2288.754m^2[/tex]
