To find the area of a triangle when you know the lengths of two sides and the included angle, you can use the formula:
\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \]
where \( a \) and \( b \) are the lengths of the two sides, and \( C \) is the included angle in degrees.
In this case:
- \( a = 26 \) feet
- \( b = 32 \) feet
- \( C = 98 \) degrees
Now, we can substitute these values into the formula.
First, we need to find \( \sin(98^\circ) \). Using a calculator:
\[ \sin(98^\circ) \approx 0.985 \]
Now, we can calculate the area:
\[ \text{Area} = \frac{1}{2} \times 26 \times 32 \times \sin(98^\circ) \] \[ \text{Area} = \frac{1}{2} \times 26 \times 32 \times 0.985 \] \[ \text{Area} = \frac{1}{2} \times 832 \times 0.985 \] \[ \text{Area} = 416 \times 0.985 \approx 409.36 \text{ square feet} \]
To convert this area to square inches, recall that there are 144 square inches in a square foot:
\[ \text{Area in square inches} = 409.36 \text{ sq ft} \times 144 \text{ sq in/sq ft} \] \[ \text{Area in square inches} \approx 58943.84 \text{ square inches} \]
Rounding this to the nearest square inch, we get:
\[ \text{Area} \approx 58944 \text{ square inches} \]
Thus, the area of the triangular flower bed is approximately 58944 square inches.
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