To determine how much shelving paper Jasmira needs to buy for all three shelves, we first need to find the area of one triangular shelf and then multiply that area by three.
Given:
- Side \( a = 22 \) inches
- Side \( b = 35 \) inches
- Angle \( \theta = 87^\circ \)
The area \( A \) of a triangle given two sides and the included angle can be calculated using the formula:
\[ A = \frac{1}{2}ab \sin(\theta) \]
Now, plug in the values:
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Convert the angle to radians if necessary, but since most calculators can take degrees directly, we can use: \[ \sin(87^\circ) \approx 0.998 \]
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Calculate the area of one shelf: \[ A = \frac{1}{2} \times 22 \times 35 \times \sin(87^\circ) \] \[ A \approx \frac{1}{2} \times 22 \times 35 \times 0.998 \] \[ A \approx \frac{1}{2} \times 770 \times 0.998 \approx 385 \times 0.998 \approx 384.53 \text{ inches}^2 \]
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Now, multiply by 3 to find the total area for three shelves: \[ \text{Total Area} = 3 \times 384.53 \approx 1153.59 \text{ inches}^2 \]
Rounding to the nearest square inch: \[ \text{Total Area} \approx 1154 \text{ inches}^2 \]
Given the responses provided, the closest option is:
1,153 inches².
1 answer