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
To find the area of the triangular flower bed, we can use the formula:
Area = (1/2) * a * b * sin(C)
where a and b are the lengths of the two adjoining sides, and C is the angle formed between those sides.
Plugging in the given values:
a = 26 feet
b = 32 feet
C = 98 degrees
Converting the angle to radians:
C = 98 * (π/180) radians
Calculating the area:
Area = (1/2) * 26 * 32 * sin(98 * π/180)
≈ 0.5 * 26 * 32 * sin(1.705793)
≈ 0.5 * 26 * 32 * 0.98462582405
≈ 405.067 square feet
To convert the area to square inches, we know that 1 square foot is equal to 144 square inches. Therefore:
Area = 405.067 * 144
≈ 58394.248 square inches
The area of their triangular flower bed is approximately 58394.248 square inches.