Optimizing Rear-View Mirror Dimensions for Full Rear Window Visibility

[map7s]

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 0.61 m from the driver's eyes, and 1.37 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?


I tried setting up triangles to solve this but it got very confusing, because I did not know what the legs would be for many of the dimensions. I mainly need help in getting started.

 

[Stainsor]

Try the set of triangles drawn in the attachment. Draw and label horizontal and vertical lines for each distance you know. And try and work out all of the other distances and angles.

Notice that if you grabbed the point of the triangle at the eye and swung it around to the left you would have one big triangle. In other words, the angles which look the same are the same.

You will need to use this diagram as both a side view and a top view.
For instance, with the side view, the vertical line on the left represents the mirror height and the vertical line on the right represents the rear window height (a distance of 0.3m).

With the top view, the vertical line on the left represents the mirror width and the vertical line on the right represents the rear window width (a distance of 1.3m).


I believe the easiest way to find the height and width of the mirror will be using what you know about "similar triangles".

 

[map7s]

Thank you soooo much! That made a lot of sense and it really helped!