To find the area of one oblique triangle shelf, we can 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.
In this case:
- \(a = 22\) inches
- \(b = 35\) inches
- \(C = 87^\circ\)
First, we need to calculate the area of one triangle:
-
Calculate \(\sin(87^\circ)\):
- Using a calculator, \(\sin(87^\circ) \approx 0.998\).
-
Now substitute the values into the area formula: \[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times \sin(87^\circ) \] \[ \text{Area} \approx \frac{1}{2} \times 22 \times 35 \times 0.998 \] \[ \text{Area} \approx \frac{1}{2} \times 770 \times 0.998 \] \[ \text{Area} \approx 385 \times 0.998 \approx 384.13 \text{ square inches} \]
Now, we need the area for all 3 shelves: \[ \text{Total area for 3 shelves} = 3 \times 384.13 \approx 1152.39 \text{ square inches} \]
Rounding to the nearest square inch, the total area is approximately: \[ \text{Total area} \approx 1152 \text{ square inches} \]
Therefore, Jasmira needs to buy approximately \(1,153\) inches² of shelving paper.
The correct answer is: 1,153 inches².