Trig help - split - lighthouse

[GMCBoii]

A lighthouse is situated 200m from a straight shoreline. The light rotates clockwise at 2 revolutions per minute. At what speed is the beam of light moving along the shore when the angle between the beam and the nearest point on the shore is 30 degree?

Would you solve with 30 degree or 60 degree and why?

 

[lev888]

A lighthouse is situated 200m from a straight shoreline. The light rotates clockwise at 2 revolutions per minute. At what speed is the beam of light moving along the shore when the angle between the beam and the nearest point on the shore is 30 degree?

Would you solve with 30 degree or 60 degree and why?

Please draw a diagram, post it, then we can discuss which angle should be used.

 

[GMCBoii]

Please draw a diagram, post it, then we can discuss which angle should be used.

 

[Dr.Peterson]

You can use either angle (not initially its specific value, but using it as a variable).

I personally would prefer to use an angle at the lighthouse, rather than at the shore, because the former is what is directly described (rotation of the beam). It is the fact that the two angles are related linearly that allows either to be used, as each is changing at the same constant rate.

 

[GMCBoii]

You can use either angle (not initially its specific value, but using it as a variable).

I personally would prefer to use an angle at the lighthouse, rather than at the shore, because the former is what is directly described (rotation of the beam). It is the fact that the two angles are related linearly that allows either to be used, as each is changing at the same constant rate.

The last part where I substitute in angles is where its confusing me. So because the question "when the angle between the beam and the nearest point on the shore is 30 degree", does that mean I use 30?

 

[Dr.Peterson]

You never explicitly defined [MATH]\theta[/MATH]; but clearly you intend it to be the angle where you wrote 30. After differentiating, you replace [MATH]\theta[/MATH] with its specified value, which is 30 degrees.

If I had defined [MATH]\theta[/MATH] to be the other acute angle in the triangle, then after differentiating [MATH]x = 200\tan(\theta)[/MATH], I would replace [MATH]\theta[/MATH] with its value, which would be 60.

 

[GMCBoii]

You never explicitly defined [MATH]\theta[/MATH]; but clearly you intend it to be the angle where you wrote 30. After differentiating, you replace [MATH]\theta[/MATH] with its specified value, which is 30 degrees.

If I had defined [MATH]\theta[/MATH] to be the other acute angle in the triangle, then after differentiating [MATH]x = 200\tan(\theta)[/MATH], I would replace [MATH]\theta[/MATH] with its value, which would be 60.

Thanks you're very helpful