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To find the height of the Eiffel Tower, Antoine placed a mirror of 500 meters away from the tower. He then positions himself so the top of the tower is visible in the mirror. He is standing 2.75 meters from the mirror and his eyes are 1.8 meters off the ground. How tall is the tower?

 Mar 4, 2020
 #1
avatar+109499 
+2

This  will  follow  the principle  that  the angle  of incidence of the light beam  =  the  angle  of  reflection  of the light beam

 

We can solve this by using similar triangles such  that.....

 

1.8 /  2.75  =   height  of tower  / 500         cross-multiply

 

500 * 1.8 / 2.75  = height of tower  ≈  327.3  m

 

Proof

 

arctan( 373.3 / 500)  = 33.2°   =  angle of incidence

 

arctan   ( 1.8/ 2.75)  = 33.2°  = angle of reflection

 

 

cool cool cool

 Mar 5, 2020
edited by CPhill  Mar 5, 2020
edited by CPhill  Mar 5, 2020
 #2
avatar+22043 
+1

Nice work , Chris !   

ElectricPavlov  Mar 5, 2020
 #3
avatar+109499 
0

THX, EP!!!

 

 

cool cool cool

CPhill  Mar 5, 2020

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