Final answer:
To find the length of WY in ΔXYZ with given angles and side, we utilized the sine function in the right triangle ΔXWY. By applying sin(51°) = WY/XW and inserting the given values, we determined that the length of WY is approximately 70.76.
Step-by-step explanation:
We are asked to find the length of WY to the nearest hundredth in triangle ΔXYZ, where ∠Y=90°, ∠X=51°, and ∠ZWY=72° with a given length of XW=91.
Since ∠Y is a right angle and ∠X is given, we can find ∠Z in ΔXYZ by using the fact that the sum of angles in a triangle equals 180°.
Therefore, ∠Z = 180° - 90° - 51°
= 39°.
In triangle ΔZWY, we already have ∠ZWY = 72°, and since ∠WYZ is shared with ΔXYZ, it is also 39°, and by extension, ∠WY is also 39°.
To find WY, we can utilize the sine function in the right triangle ΔXWY:
sin(∠X) = opposite/hypotenuse
sin(51°) = WY/XW
sin(51°) * XW = WY
WY ≈ sin(51°) * 91
WY ≈ 0.7771 * 91
WY ≈ 70.76
Therefore, the length of WY is approximately 70.76 to the nearest hundredth.