Question

Triangle X Y Z is shown. Angle Y X Z is a right angle. The length of Y X is 12 inches and the length of X Z is 10 inches. Angle X Y Z is x.
Which is the best approximation for the measure of angle XYZ?

33.6°
39.8°
50.2°
56.4°

Answer 1

Angle at Y has tangent = (opposite)/(adjacent) = XZ/YX = 10/12 = 5/6.
x = arctan(5/6) ≈ 39.8°.

So the best approximation is 39.8°.