The rear window in a car is approximately a rectangle, 1.0 m wide and 0.29 m hig

Question

The rear window in a car is approximately a rectangle, 1.0 m wide and 0.29 m high. The inside rearview mirror is 0.54 m from the driver's eyes, and 1.62 m from the rear window.

A )What is the minimum length for the rearview 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?

B) What is the minimum height for the rearview 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?

Explanation / Answer

Here we have to equate the angle of viewing
(a)So for length the angle made by the rear window
tan(theta) = WW/(XD+XR) where XD is the distance of driver from mirror and XR is the distance of rear window from the driver and Ww is width of the window.
and when we see the angle for the image
tan(theta) = W/(XD)
so equating both equation
W = WWXD(XD+XR) = 1*(0.54)/(0.54+1.62) = 0.25 m
(b) Similarly for height
H = HWXD/(XD+XR) =0.0725 m

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