Final Answer:
In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.C. WY = 101, mZ = 132°.
Step-by-step explanation:
To find the length of WY and the measure of angle Z, we can use trigonometric relationships in a right-angled triangle. Let's denote the length of side WY as 'a' and the measure of angle Z as 'b'. According to the given options:
Option A: WY = 72, mZ = 132°
Option B: WY = 101, mZ = 72°
Option C: WY = 101, mZ = 132°
Option D: WY = 132, mZ = 101°
We need to find the option that satisfies the trigonometric relationship in a right-angled triangle. The most common trigonometric relationship in this case is the tangent of an angle, which is the ratio of the opposite side to the adjacent side.
tan(b) = Opposite/Adjacent
In a right-angled triangle with angle Z, tan(b) = WY / ZX.
Now, let's evaluate each option:
Option A: tan(132°) = 72 / ZX
Option B: tan(72°) = 101 / ZX
Option C: tan(132°) = 101 / ZX
Option D: tan(101°) = 132 / ZX
Comparing the ratios, we find that option C is the correct solution as it satisfies the given trigonometric relationship. Therefore, WY = 101 and mZ = 132°.