Magnetic Forces and Magnetic Fields?

Question

When a charged particle moves at an angle of 25 degrees with respect to a magnetic field, it experiences a magnetic force of magnitude F. At what angle (less than 90 degrees) with respect to this field will this particle, moving at the same speed, experience a magnetic force of magnitude 2F?

Answer 1

sin(25) = (1/2)*sin(unknown)

about 58 degrees?

Check my work!

Answer 2

F = q v B sin(θ1)

F = q v B sin(25) =====>1

q is the charge of the particle

v is velocity

B is the magnitude of the magnetic field

in your question q is constant as it's the same particle in the 2 statements

v is constant "moving at the same speed"

B is also constant as it's the same magnetic field

that mean that any change will be only in the angle

So the second statement will be

2F=q v B sin(θ2) =====> 2

F = q v B sin(25) =====>1

divide 2 by 1

2 = sin(θ2) \ sin(25)

sin(θ2) = 2 sin(25) = 0,8452365235

Using calculator

θ2 = 57° 41'  50,23''

approximately

θ2 = 58°