Jasmine has a new corner shelving unit that is triangular. The unit has three identical oblique triangle shelves. Jasmine wants to put some shelving paper down but isn't sure how much to buy. If one side of each triangle is 24 inches, an adjoining side is 29 inches, and the angle formed between them is 83 degrees, then how much paper (to the nearest square inch) does she need to cover all 3 shelves.
To find the area of each triangular shelf, we can use the formula:
Area = (1/2) * (base) * (height)
First, we need to find the height of each triangle. We can use the given information to find the height using the sine function.
sin(angle) = opposite/hypotenuse
sin(83 degrees) = height/24 inches
height = sin(83 degrees) * 24 inches
height ≈ 23.567 inches
Now, we can find the area of each triangular shelf:
Area = (1/2) * 24 inches * 23.567 inches
Area ≈ 283.404 square inches
Since there are 3 identical triangular shelves, Jasmine needs to buy:
3 * 283.404 square inches ≈ 850.212 square inches
Therefore, Jasmine needs to buy approximately 850 square inches of shelving paper to cover all 3 shelves.
the anwsers you can pick from are 2,088inches squared,
348 inches squared,
1,036 inches squared,
2,072 inches squared.
We made an error in our calculations. Let's redo the calculations correctly.
To find the area of each triangular shelf, we can use the formula:
Area = (1/2) * (base) * (height)
First, we need to find the height of each triangle. We can use the given information to find the height using the cosine function.
cos(angle) = adjacent/hypotenuse
cos(83 degrees) = height/24 inches
height = cos(83 degrees) * 24 inches
height ≈ 5.085 inches
Now, we can find the area of each triangular shelf:
Area = (1/2) * 29 inches * 5.085 inches
Area ≈ 73.677 square inches
Since there are 3 identical triangular shelves, Jasmine needs to buy:
3 * 73.677 square inches ≈ 221.031 square inches
Therefore, Jasmine needs to buy approximately 221 square inches of shelving paper to cover all 3 shelves.
None of the provided answer choices match the correct result.