Optimizing Rear-View Mirror Dimensions for Full Rear Window Visibility

AI Thread Summary
To determine the minimum dimensions for the rear-view mirror, the geometry of the setup must be analyzed, focusing on the angles formed between the driver's eyes, the mirror, and the corners of the rear window. The mirror needs to be wide enough to capture the full width of the rear window while maintaining the required distance from the driver's eyes. A visual representation can help clarify the relationships between the distances involved, particularly using triangles to represent the lines of sight. The key is to calculate the necessary width of the mirror based on these geometric principles. Understanding these dimensions ensures the driver can see the entire rear window without head movement.
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Homework Statement


The rear window in a car is approximately a rectangle, 1.3 m wide and 0.30 m high. The inside rear-view mirror is 0.62 m from the driver's eyes, and 1.58 m from the rear window. What are the minimum dimensions for the rear-view mirror if the driver is to be able to see the entire width and height of the rear window in the mirror without moving her head?


Homework Equations


None really - other than regular geometry stuff like tan theta = y/x, etc.


The Attempt at a Solution


I have none, I've been trying to draw this thing and make triangles or something but I'm completely lost.

Thanks in advance for any help!
 
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Forget that it's a mirror and draw the rear window the correct distance in front of the driver, now draw the mirror as a slot restricting the width - how wide does it have to be to get the lines from the driver to the corners of the 'rear' mirror?
 
Yes! Thank you, :-).
 

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