Final Answer:
Given the angle m∠ZE = 64° and sides g = 9 and e = 10, the Sine Law allows for two possible triangles, satisfying the conditions. Thus, the correct answer is option C. Two triangles
Step-by-step explanation:
When given a side (g = 9) and two angles (m∠ZE = 64° and e = 10), we can use the Sine Law to determine the possible triangles. The Sine Law states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. For a triangle with sides a, b, and c, and angles A, B, and C opposite to these sides, the Sine Law is expressed as:
a / sin A = b \ sin B = c \ sin C
In this case, we have g = 9, m∠ZE = 64°, and e = 10. To find the possible triangles, we consider two scenarios: one where \( \sin A \) corresponds to the given angle m∠ZE = 64°, and the other where \( \sin A \) corresponds to the angle opposite side g.
For the given angle m∠ZE = 64°, there are two possible solutions for side e = 10, resulting in two triangles. Therefore, the correct answer is C. Two triangles.
Thus, the correct answer is option C. Two triangles