Final answer:
To find the area of a triangle, we can use the formula: Area = (1/2) * base * height. First, we need to find the height using trigonometry. Then, we can use the formula to calculate the area.
Step-by-step explanation:
To find the area of triangle NOP, we can use the formula:
Area = (1/2) * base * height
First, we need to find the height of the triangle. Since we have the length of one side (OP) and the measure of one angle (∠N), we can use trigonometry to find the height:
Sin(∠N) = height / OP
height = Sin(∠N) * OP
Substituting the given values:
height = Sin(138°) * 23 cm
Next, we can calculate the area:
Area = (1/2) * 92 cm * (Sin(138°) * 23 cm)
Rounding to the nearest square centimeter, the area of triangle NOP is approximately 908 square centimeters.