Answer:
m ∠ W is 58.2°
Step-by-step explanation:
Given:
XY = 15
WZ = 22
∠ XZY =25°
To Find:
m ∠ W = ?
Solution:
In right angle triangle Δ XZY, by Sine identity we have
[tex]\sin Z= \frac{\textrm{side opposite to angle Z}}{Hypotenuse} \\\sin 25= \frac{XY}{XZ}\\0.4226=\frac{15}{XZ}\\\therefore XZ=\frac{15}{0.4226} \\XZ=35.49[/tex]
∴ XZ = 35.49
Now in right angle triangle Δ WZX, by tangent identity we have
[tex]\tan W = \frac{\textrm{side opposite to angle Z}}{\textrm{side adjacent to angle Z}}\\\tan W = \frac{XZ}{WZ}\\\tan W = \frac{35.49}{22}\\\tan W = 1.6131\\\therefore W =\tan^{-1}(1.6131) \\W= 58.2\°[/tex]
∴m ∠W =58.2°
