To find the area of one triangular shelf, we can use the formula for the area of a triangle when we know two sides and the included angle:
\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \]
where \(a\) and \(b\) are the lengths of the two sides, and \(C\) is the included angle.
Given:
- Side \(a = 22\) inches
- Side \(b = 35\) inches
- Angle \(C = 87\) degrees
First, we need to calculate \( \sin(87^\circ) \):
\[ \sin(87^\circ) \approx 0.998 \]
Now we can plug in the values into the area formula:
\[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times \sin(87^\circ) \] \[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times 0.998 \] \[ = \frac{1}{2} \times 770 \times 0.998 \] \[ = 385 \times 0.998 \approx 384.23 \text{ square inches} \]
Now, this is the area of one triangular shelf. Since Jasmira has three identical shelves, we multiply the area by 3:
\[ \text{Total Area} = 3 \times 384.23 \approx 1152.69 \text{ square inches} \]
Rounding to the nearest square inch gives us:
\[ \text{Total Area} \approx 1153 \text{ square inches} \]
None of the provided options match exactly, but the closest value is:
O 1, 153 inches².
Thus, Jasmira should buy enough shelving paper to cover approximately 1,153 inches².
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