Jasmira has a new corner shelving unit that is triangular. The unit has three identical oblique triangle shelves. Jasmira wants to put some shelving paper down but isn’t sure how much to buy. If one side of each triangle is 22 inches, an adjoining side is 35 inches, and the angle formed between them is 87 degrees, then how much paper (to the nearest square inch) does she need to cover all 3 shelves?(1 point) Responses 2,038 inches2 2,038 inches squared 1,153 inches2 1,153 inches squared 660 inches2 660 inches squared 1,647 inches2
To find the area of each triangle shelf, we can use the formula for the area of an oblique triangle: A = 0.5 * a * b * sin(C), where a and b are the lengths of the sides and C is the angle between them.
For the first triangle, the sides are 22 inches and 35 inches, and the angle is 87 degrees:
A1 = 0.5 * 22 * 35 * sin(87) ≈ 660 inches²
Since all three triangle shelves are identical, the total area of paper needed to cover all three shelves is:
Total area = 3 * 660 inches² = 1980 inches²
Rounded to the nearest square inch, Jasmira needs 1980 inches² or 2,038 inches² of paper. Therefore, the answer is 2,038 inches².