How can I calculate the angle of a tilted mirror to see my reflection?

AI Thread Summary
To calculate the angle at which the mirror should be tilted to see the reflection of your eyes, first establish the geometry of the situation using right triangles. The height difference between your eyes and the mirror, along with your distance from the wall, will help determine the necessary angles. The angle of incidence equals the angle of reflection, so you can use the previously calculated angle for your shoes as a reference. By setting up a second triangle for your eyes, you can apply trigonometric functions to find the required angle of tilt for the mirror. Understanding these relationships will allow you to solve for the angle effectively.
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Homework Statement



You stand 1.80 m in front of a wall and gaze downward at a small vertical mirror mounted on it. In this mirror you can see the reflection of your shoes. If your eyes are 1.95 m above your feet, through what angle should the mirror be tilted for you to see your eyes reflected in the mirror? (The location of the mirror remains the same, only its angle to the vertical is changed.)


I know that the angle of incidence is equal to the angle of refraction and I tried creating triangles to solve this problem. For the first case, where you can see your shoes, when I drew the triangle, it was isoceles, so I split it up into to equal right triangles and found that the angles of incidence and refraction were about 62 degrees, but I did not know where to go from there or if I was even on the right track.
 
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thats pretty much the whole problem. now that you know what angle the mirror is set at, figure out what angle the mirror should be set at to see your eyes and subtract
 
that was just what I was wondering - how can I set up that second triangle with the angle of the mirror? I only know the value of one side (the distance), so how can I solve for the angle?
 
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