Question

Jasmina has a new comer shelving unit that is triangular shelves. Jamira wants to put some shelving paper down but isn't sure how much to buy. If one side of each triangle is 22 inches, an adjoining side is 35 inches, and the angle formed between them is 87 degrees, then how much paper( to the nearest square I ch) does she need to cover all 3 shelves?

Answer 1

To find the area of one triangular shelf, 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 in degrees.

In this case:
- \( a = 22 \) inches,
- \( b = 35 \) inches,
- \( C = 87^\circ \).

First, we calculate the sine of \( 87^\circ \):

\[
\sin(87^\circ) \approx 0.998
\]

Now we can substitute the values into the area formula:

\[
\text{Area} = \frac{1}{2} \times 22 \times 35 \times \sin(87^\circ)
\]

Calculating the area step by step:

1. Calculate \( 22 \times 35 \):

\[
22 \times 35 = 770
\]

2. Now calculate \( \frac{1}{2} \times 770 \):

\[
\frac{1}{2} \times 770 = 385
\]

3. Multiply by \( \sin(87^\circ) \):

\[
\text{Area} \approx 385 \times 0.998 \approx 384.3 \text{ square inches}
\]

Since there are 3 shelves, we multiply by 3:

\[
\text{Total Area} = 3 \times 384.3 \approx 1152.9 \text{ square inches}
\]

Finally, rounding to the nearest square inch:

\[
\text{Total Area} \approx 1153 \text{ square inches}
\]

Jasmina needs to buy approximately **1153 square inches** of shelving paper to cover all 3 shelves.