Answer: it will cost $3190.752
Step-by-step explanation:
Step 1
We would determine the length of the side of the field, AC. To do this, we would apply the cosine rule. Since we know sides AB and BC and angle B, It will be expressed as
b^2 = a^2 + c^2 - 2acCosB. It becomes
b^2 = 320^2 + 450^2 - 2×320×450Cos80
= 102400 + 202500 - 144000Cos80
= 304900 - 24998.4
b^2 = 279901.6
b= √279901.6
b = 529.06 yards
Step 2
We would determine the area of the triangle. The formula for the area of the triangle is expressed as
Area of triangle = 1/2 × acSinB
Area of triangle = 1/2 × 320 × 450 × Sin 80
Area of triangle = 72000 × 0.9848 = 70905.6 yards^2
If 100 square yards cost $4.50
70905.6 square yards cost (70905.6×4.5) /100 = $3190.752
