malachi and talia are refreshing a trianglular flower bed at their school. they want to know the area, so they know the amount of material they need. they know two adjoining sides measure 26 feet and 32 feet, and the angle formed between those sides measures 98 degrees. what is the area of their triangular flower bed to the nearest square inch if inches^2
To find the area of the triangular flower bed, we can use the formula:
Area = (1/2) * (side1) * (side2) * sin(angle)
Given that the two adjoining sides measure 26 feet and 32 feet, and the angle formed between those sides measures 98 degrees, we can substitute these values into the formula:
Area = (1/2) * (26 ft) * (32 ft) * sin(98°)
To find the area in square inches, we need to convert from square feet to square inches. Since 1 foot is equal to 12 inches, we can convert the area by multiplying the area calculated above by (12 in/1 ft)^2:
Area = (1/2) * (26 ft) * (32 ft) * sin(98°) * (12 in/1 ft)^2
Using a calculator to evaluate this expression accurately, we find that the area of their triangular flower bed is approximately 3678 square inches.