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 0.50 m from the driver’s eyes and 1.50 m from the rear window. What are the minimum dimensions that the rear-view mirror should have 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?

Height of mirror 0.075 m

width of mirror 0.325 m  

Explanation:

given data

wide = 1.3 m

high = 0.30 m

driver’s eyes = 0.50 m

rear window = 1.50 m

solution

we take here height / width of the mirror  is

height / width   =   .................1

and

height /width of the window is

height /width  =   .................2

and

distance of eye / window by the mirror is

distance of eye / window =      .................3

so here

θ = θi  = θr    ....................4

and  tanθ for vertical is

tanθ  =  

tanθ  =         ....................5

so

h =       ....................6

put  here value and we get

h = 0.075 m

and

when we take here tanθ for horizontal than it will be

tanθ =    

tanθ =       .......................7

so

        ....................8

put here value and we get

w = 0.325 m