Malachi and Talia are refreshing a triangular 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?(1 point)
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 between those sides.
In this case, 'a' = 26 feet, 'b' = 32 feet, and C = 98 degrees.
Plugging in these values into the formula, we have:
Area = (1/2) * 26 * 32 * sin(98)
Using a calculator, we find that sin(98) ≈ 0.98480775301.
Therefore, the area of the triangular flower bed is approximately:
Area ≈ (1/2) * 26 * 32 * 0.98480775301
Area ≈ 416.10212247664 square feet
To convert this to square inches, we know that 1 square foot is equal to 144 square inches.
Therefore, the area of the triangular flower bed is approximately:
Area ≈ 416.10212247664 * 144 square inches
Area ≈ 59,875.372035638016 square inches
Rounded to the nearest square inch, the area of the triangular flower bed is:
Area ≈ 59,875 square inches