Why Are the Angles Theta Equal in Inclined Planes?

[yougene]

Homework Statement

By what relation/reasoning are these two angles, theta, the same?





http://img198.imageshack.us/img198/6273/inclinedplane.jpg

 

[emyt]

Homework Statement

By what relation/reasoning are these two angles, theta, the same?





http://img198.imageshack.us/img198/6273/inclinedplane.jpg

[/URL]

similar triangles?

 

[yougene]

By what reasoning?

 

[emyt]

well, a triangle is determined by 2 of its angles or the ratio between its sides; the two triangles could share a common angle if the other two angles are the same for instance (in this case, the 90 degrees and something else), or the length of the "sides" could be 1.5 / 2 = 3 /4

 

[yougene]

The only features I can discern here, are two parallel lines( ceiling and base of triangle ), the sides of the incline, and the inclines angle Theta. Other than the parallel ceiling there is nothing that relates the rope to the incline.

In my mind if I move the strings hanging point left or right I see the angle changing. If I make the string longer or shorter I see the angle changing.

Am I missing something here?

 

[Hurkyl]

The angles are equal for the same reason that the wedge's height is 3 meters -- that's just the problem you're given.

 

[emyt]

The only features I can discern here, are two parallel lines( ceiling and base of triangle ), the sides of the incline, and the inclines angle Theta. Other than the parallel ceiling there is nothing that relates the rope to the incline.

In my mind if I move the strings hanging point left or right I see the angle changing. If I make the string longer or shorter I see the angle changing.

Am I missing something here?

if you pulled the block back, the "adjacent" and hypotenuse sides of the triangle formed by the string and an imagined line would be stretched, and that would eliminate the common ratio of sides between the triangle and the imaginary triangle from the string. but the question gives you this information, at that position, the imaginary triangle and the actual triangle become similar triangles.

 

[yougene]

That's what I'm thinking as well, thanks guys.

If anyone has a third opinion let me know.

 

[mikelepore]

They're saying that the block happens to be at particular location, and the cord happens to have a particular length, where it becomes true that the two angles are equal.