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)

Question

Responses

660 inches2
660 inches squared

1,647 inches2
1,647 inches squared

1,153 inches2
1,153 inches squared

2,038 inches2
2,038 inches squared

Answer 1

To find the area of one of the triangular shelves, we will use the formula for the area of a triangle given two sides and the included angle:

\[ \text{Area} = \frac{1}{2}ab\sin(C) \]

where \(a\) and \(b\) are the lengths of the two sides, and \(C\) is the included angle.

Given:

• \(a = 22\) inches
• \(b = 35\) inches
• \(C = 87^\circ\)

First, we need to calculate \(\sin(87^\circ)\).

Using a calculator, \[ \sin(87^\circ) \approx 0.998 \]

Now, we can substitute these values into the area formula:

\[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times \sin(87^\circ) \] \[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times 0.998 \] \[ \text{Area} \approx \frac{1}{2} \times 22 \times 35 \times 0.998 \approx 385.3 \text{ square inches} \]

Now we need to calculate the total area for all three shelves:

\[ \text{Total Area} = 3 \times 385.3 \approx 1155.9 \text{ square inches} \]

Rounding to the nearest square inch:

\[ \text{Total Area} \approx 1156 \text{ square inches} \]

Looking at the responses provided, it seems that the answer is closest to:

1,153 inches²

Therefore, the correct amount of shelving paper she needs to buy is:

1,153 inches²