Final answer:
The area of triangle WXY can be found using the formula for the area of a triangle and trigonometry. The base is 32 inches and the height can be found using the sine function. Plug in the values to calculate the area in square inches.
Step-by-step explanation:
To find the area of triangle WXY, we can use the formula for the area of a triangle:
Area = 1/2 * base * height.
In this case, the base is XW, which is 32 inches, and the height is the perpendicular distance from the base to the vertex, which is YW. The angle WZX is given as 16 degrees, so we need to find the height using trigonometry.
We can use the sine function to find the height h. Since we know the angle and the side opposite the angle, we can use the formula sin(angle) = opposite/hypotenuse.
Rearranging the formula, we have height = opposite / sin(angle).
Plugging in the values, we get height = 96 / sin(16)
Now that we have the base and the height, we can calculate the area of the triangle as 1/2 * 32 * (96 / sin(16)). This gives us the area in square inches.