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Kiran is visiting the Statue of Liberty. He wants to test the mirror method of indirect measurement for calculating heights. He is 5.8 feet tall and knows that the Statue of Liberty is 305 feet tall. Sketch a diagram showing where a mirror could be placed to use similar triangles to verify the height of the Statue of Liberty. Make sure to include the distance from Kiran to the mirror and the distance from the mirror to the Statue of Liberty.

 

(You don't have to make a diagram but it would help me better. I'm confused about where I have to start so I would like to see how to solve this problem step by step.)

 Nov 3, 2019
 #1
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Let the top of the statue  be point A

Let the bottom be point B

Place  the mirror between Kiran and the statue such that from  Kiran's point of view, the whole statue shows in the mirror....call this  point, C

Call the top of Kiran's head point D

Call the place where he stands  point E

 

Because  the angle of  incidence of light  = its angle of reflection, then angle ACB   =Angle DCE

And Angle  ABC  =  Angle DEC  = right angles

So..........by AA congruency.....triangle  ABC  is similar to triangle DEC

 

Here's the idea   {using a palm tree rather than a statue ]  : 

 

 

Now....note something else.....if the mirror is placed  305 ft from the statue = BC   and Kiran stands exactly 5.8 ft from the mirror = EC....we have this relationship

 

AB / BC  =   DE / EC

 

305 / 305  =  5.8  / 5.8

 

Which is true

 

Furthermore

The tangent of angle ACB [ angle of incidence]  =   AB / BC  = 305/305  =  1

And

The tangent of  angle DCE  [angle of reflection ]  = 5.8 / 5.8  = 1

So....since the tangents are equal.....then  we know that the angle of  incidence  = angle of reflection

 

 

cool cool cool

 Nov 3, 2019

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