To find the area of each oblique triangle shelf and then determine how much shelving paper Jasmira needs for all three shelves, we can use the formula for the area of a triangle given 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,
- \( C \) is the included angle between those two sides.
Given:
- \( a = 22 \) inches
- \( b = 35 \) inches
- \( C = 87^\circ \)
First, we need to calculate the area of one triangle. We will calculate the sine of 87 degrees to use in our formula:
Using a calculator: \[ \sin(87^\circ) \approx 0.998 \]
Now substituting into the area formula: \[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times \sin(87^\circ) \]
Calculating step-by-step:
- Calculate \( 22 \times 35 = 770 \).
- Then, multiply by \( \sin(87^\circ) \): \[ 770 \times 0.998 \approx 766.46 \]
- Now calculate the area: \[ \text{Area} = \frac{1}{2} \times 766.46 \approx 383.23 , \text{inches}^2 \]
This is the area of one triangle. Since Jasmira has three identical triangular shelves: \[ \text{Total Area} = 3 \times 383.23 \approx 1149.69 , \text{inches}^2 \]
Rounding to the nearest whole number gives \( 1,150 , \text{inches}^2 \).
None of the answer options exactly match this value, so let's check the choices again:
- 1,153 inches²
- 2,038 inches²
- 660 inches²
- 1,647 inches²
The closest option is 1,153 inches².
Thus, Jasmira should buy 1,153 inches² of shelving paper.