How do similar triangles help determine the visible area in a plane mirror?

[Wing2015]

Homework Statement

How much of a wall 3m behind you can be observed in a 5 cm square mirror which is held centrally at a distance of 10 cm from your eye?

Homework Equations

None that I can think of. I think this is straight geometry.

The Attempt at a Solution

I know I have to use similar triangles but don't understand why. What's the rule of thumb for using similar triangles? Is it because the eye is in common between the wall and mirror? How do I know the two triangles share the same angles?

This is the answer in the book:

Let the highest part of the wall able to be seen be x metres above the top of the mirror.

From similar triangles:
X/300 =2.5\10
X=75 cm

You can see a square of the wall of length 75+5+75=155cm

Now I think I understand why the second similar triangles side length is 2.5cm ( the mirror was placed centrally hence 5cm/2) but can you explain why 75 is added twice and then to the length of the full mirror in the last part? I'm really lost.

Any help would be appreciated. Thanks!

[/B]

 

[Dick]

Homework Statement

How much of a wall 3m behind you can be observed in a 5 cm square mirror which is held centrally at a distance of 10 cm from your eye?

Homework Equations

None that I can think of. I think this is straight geometry.

The Attempt at a Solution

I know I have to use similar triangles but don't understand why. What's the rule of thumb for using similar triangles? Is it because the eye is in common between the wall and mirror? How do I know the two triangles share the same angles?

This is the answer in the book:

Let the highest part of the wall able to be seen be x metres above the top of the mirror.

From similar triangles:
X/300 =2.5\10
X=75 cm

You can see a square of the wall of length 75+5+75=155cm

Now I think I understand why the second similar triangles side length is 2.5cm ( the mirror was placed centrally hence 5cm/2) but can you explain why 75 is added twice and then to the length of the full mirror in the last part? I'm really lost.

Any help would be appreciated. Thanks!
[/B]

Because you want the total size of the square. You can see 75cm above the top of the mirror and 75cm below the bottom. Add the 5cm size of the mirror and you're done.

 

[mfb]

Those problems are much easier to understand if you draw a sketch.

 

[Wing2015]

Thanks for your replies! I get it now. There was a problem with the way I sketched the problem which was the reason why I wasn't able to understand.

Cheers