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
1,153 inches2
1 comma 153 inches squared
660 inches2
660 inches squared
1,647 inches2
1 comma 647 inches squared
2,038 inches2
To calculate the total area of the three shelves, we need to calculate the area of each triangle shelf and then multiply it by 3.
To find the area of a triangle, we can use the formula: (1/2) * base * height.
The height of each triangle can be found using the sine function: sin(angle) = opposite/hypotenuse.
In this case, the angle is 87 degrees and the opposite side is the height of the triangle. So, the height of each triangle is 35 * sin(87) = 34.9999 (rounded to 5 decimal places).
The base of each triangle is 22 inches.
Now, we can calculate the area of each triangle: (1/2) * 22 * 34.9999 = 384.99952 (rounded to 5 decimal places).
Since we need to find the total area of all 3 shelves, we multiply this by 3: 384.99952 * 3 = 1,154.99856 (rounded to 5 decimal places).
Therefore, Jasmira needs approximately 1,154 square inches of shelving paper to cover all 3 shelves.