Point M is outside the alpha plane, MO is perpendicular, MA is inclined to the alpha plane.

Point M is outside the alpha plane, MO is perpendicular, MA is inclined to the alpha plane. Find the angle between the plane and the line MA, if MO = 1/2 MA.

The angle between the plane and the line MA is the MAO angle. The MOA triangle is rectangular (since MO is a perpendicular), angle O = 90 degrees, MO = MA / 2 is the leg opposite to the MAO angle, MA is the hypotenuse (since it lies opposite the right angle O).
1 way. The sine of an angle in a right-angled triangle is the ratio of the opposite leg to the hypotenuse of the triangle. Find the sine of the MAO angle:
sinMAO = MO / MA;
sinMAO = (MA / 2) / MA;
sinMAO = MA / 2MA;
sinMAO = 1/2.
MAO angle = 30 degrees.
Method 2. Since the MO leg is 2 times smaller than the MA hypotenuse, it lies opposite an angle of 30 degrees, since from the properties of a right triangle it is known that opposite an angle of 30 degrees lies a leg, which is exactly 2 times smaller than the hypotenuse.
Answer: MAO angle = 30 degrees.