Triangular field where two sides mearure 450m and 320m. Angle between two sides is 80°.farmer use insecticide cost k4.50 per 100m² or any part of 100m².what will it cost to use insecticide?

First, we need to calculate the area of the triangular field using the given sides and angle. We can use the formula for the area of a triangle given two sides and the included angle:

Area = 0.5 * a * b * sin(C)

Where a and b are the lengths of the two sides and C is the angle between them in radians.

Converting the angle from degrees to radians:
80° * (π/180) = 1.3963 radians

Calculating the area:
Area = 0.5 * 450m * 320m * sin(1.3963)
Area ≈ 0.5 * 450 * 320 * 0.985
Area ≈ 70560 m²

Now, we need to calculate the cost of using insecticide for this area. The cost is K4.50 per 100m², so we divide the total area by 100 to find out how many units of 100m² are needed:

70560 m² / 100 = 705.6 units

Since the farmer can only purchase whole units of 100m², they would need to purchase 706 units. Therefore, the total cost of using insecticide would be:

706 units * K4.50 = K3177.00

So, it would cost K3177.00 to use insecticide on the triangular field.

Solving for the area of triangular field

Area of a triangle =[1/2 -base -height]
Area = [1/2 - 450m - 320m sin80°]
Area = 86400m²

we know that the farmer will use insecticide costs K4.50 per 100m² or any part of 100m²
So it will cost the farmer:
Cost of insecticide = 86400m² - k4.50/100m²
Cost of insecticide = k3888