Question

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

Answer 1

m ∠ W is 58.2°

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= (XY)/(XZ)\\0.4226=(15)/(XZ)\\\therefore XZ=(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 = (XZ)/(WZ)\\\tan W = (35.49)/(22)\\\tan W = 1.6131\\\therefore W =\tan^(-1)(1.6131) \\W= 58.2\°`

∴m ∠W =58.2°