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 = 26 feet,
b = 32 feet,
C = 98 degrees.
First, we need to convert the angle from degrees to radians:
C_radians = C * (pi/180) = 98 * (pi/180) ≈ 1.71042 radians.
So the area of the triangular flower bed is:
Area = (1/2) * 26 * 32 * sin(1.71042)
≈ 210.55 square feet.
To give the answer in square inches, we need to convert square feet to square inches. Since 1 square foot = 144 square inches:
Area = 210.55 * 144
≈ 30,312.72 square inches.
Therefore, the area of their triangular flower bed is approximately 30,313 square inches.