Answer:
The area of the field = 19966.21 units²
Step-by-step explanation:
* Lets explain how to find area of a triangle by trigonometry rule
- In any triangle if you have the lengths of two sides and the measure
of the including angle between these two sides, then the area of the
triangle is A = [tex]\frac{1}{2}s_{1}s_{2}sin\alpha[/tex] , wher α is the
including angle between them
* Lets solve the problem
∵ The field is shaped triangle
∵ The lengths of two sides of the field are 218.5 and 213.3
∴ s1 = 218.5
∴ s2 = 213.3
∵ The measure of the angle between the two sides is 58.96°
∴ α = 58.96°
- Lets find the area using the rule of trigonometry
∴ [tex]A=\frac{1}{2}(218.5)(213.3)sin(58.96)=19966.21[/tex]
∴ The area of the field = 19966.21 units²
