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.)

Guest Nov 3, 2019

#1**+1 **

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

CPhill Nov 3, 2019