To find the area of one triangle shelf, we can use the formula for the area of a triangle when two sides and the included angle are known:
\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \]
where \(a\) and \(b\) are the lengths of the sides, and \(C\) is the included angle.
Here, we have:
- \(a = 22\) inches
- \(b = 35\) inches
- \(C = 87^\circ\)
First, we calculate \(\sin(87^\circ)\):
\[ \sin(87^\circ) \approx 0.998 \]
Now we can substitute \(a\), \(b\), and \(\sin(C)\) into our area formula:
\[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times 0.998 \]
Calculating \( \frac{1}{2} \times 22 \times 35 \):
\[ \frac{1}{2} \times 22 = 11 \] \[ 11 \times 35 = 385 \]
Now substituting back into the area calculation:
\[ \text{Area} \approx 385 \times 0.998 \approx 384.53 \text{ square inches} \]
Now, since Jasmira has three identical triangular shelves, we multiply the area of one shelf by 3:
\[ \text{Total Area} = 3 \times 384.53 \approx 1153.59 \]
Rounding to the nearest square inch gives:
\[ \text{Total Area} \approx 1154 \text{ square inches} \]
Since the options provided are:
A. 660 inches^2
B. 1,153 inches^2
C. 1,647 inches^2
D. 2,038 inches^2
The closest answer is:
B. 1,153 inches^2.
1 answer