To determine how much shelving paper Jasmira needs for the three triangular shelves, we first need to find the area of one triangular shelf. To do this, 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 angle between them.
In Jasmira's case:
- \(a = 22\) inches
- \(b = 35\) inches
- \(C = 87\) degrees
First, we need to calculate \(\sin(87^\circ)\). Using a calculator, we find:
\[ \sin(87^\circ) \approx 0.998 \]
Now we can calculate the area of one triangular shelf:
\[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times 0.998 \]
Doing the multiplication:
\[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times 0.998 \approx \frac{1}{2} \times 770 \times 0.998 \approx \frac{770 \times 0.998}{2} \approx 384.85 \]
So the area of one shelf is approximately 384.85 square inches.
Since there are three identical shelves, we need to multiply the area of one shelf by 3:
\[ \text{Total Area} = 3 \times 384.85 \approx 1154.55 \text{ square inches} \]
Thus, Jasmira needs approximately 1154.55 square inches of shelving paper to cover all three shelves. To be safe, she may want to round up and buy a little extra paper.
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