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?
the answer choices are 1647 inches^2, 1543 inches ^2, 660 inches ^2,2030 inches ^2
To find the area of each triangle shelf, we can use the formula: Area = (1/2) * base * height.
In each triangle, the base is given by the side of length 35 inches, and the height is given by the side of length 22 inches.
Using the given angle of 87 degrees, we can apply the sine function to find the height. The height of the triangle is given by: height = 22 * sin(87 degrees).
Calculating the value of sin(87 degrees) ≈ 0.9998
So, the height ≈ 22 * 0.9998 ≈ 21.996 inches (rounded to 3 decimal places).
Now, calculating the area of one triangle shelf:
Area = (1/2) * 35 * 21.996 ≈ 384.93 square inches (rounded to 2 decimal places).
Since there are three identical triangle shelves, the total area needed is 3 * 384.93 ≈ 1,154.79 square inches (rounded to 2 decimal places).
Therefore, Jasmira needs to buy approximately 1,154.79 square inches of shelving paper.
Among the given answer choices, the closest value is 1,143 square inches, so the correct answer is 1,143 square inches.