Question

I need help with this tri trig I think it’s 55 but I don’t see the answer choice

Answer 1

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

$\sin Z= \frac{\textrm{side opposite to angle Z}}{Hypotenuse} \\\sin 25= \frac{XY}{XZ}\\0.4226=\frac{15}{XZ}\\\therefore XZ=\frac{15}{0.4226} \\XZ=35.49$

∴ XZ = 35.49

Now in right angle triangle Δ WZX, by tangent identity we have

$\tan W = \frac{\textrm{side opposite to angle Z}}{\textrm{side adjacent to angle Z}}\\\tan W = \frac{XZ}{WZ}\\\tan W = \frac{35.49}{22}\\\tan W = 1.6131\\\therefore W =\tan^{-1}(1.6131) \\W= 58.2\°$

∴m ∠W =58.2°