SOLUTION: sandy is trying to measure the height of a nearby flagpole using a mirror. The mirror is 6m away from the flagpole and 2 m away from sandy. If sandy is 1.5m tall how tall is the fl

Algebra ->  Trigonometry-basics -> SOLUTION: sandy is trying to measure the height of a nearby flagpole using a mirror. The mirror is 6m away from the flagpole and 2 m away from sandy. If sandy is 1.5m tall how tall is the fl      Log On


   

Question 1209173: sandy is trying to measure the height of a nearby flagpole using a mirror. The mirror is 6m away from the flagpole and 2 m away from sandy. If sandy is 1.5m tall how tall is the flagpole?
Found 2 solutions by timofer, ikleyn:
Answer by timofer(106) About Me  (Show Source):
You can put this solution on YOUR website!
Heights are distances from mirror are in proportion, similar triangles formed.
t, the flagpole height:
t%2F6=1.5%2F2
t=%286%2A1.5%29%2F2
t=3%2A1.5
t=4.5

Answer by ikleyn(52878) About Me  (Show Source):
You can put this solution on YOUR website!
.
sandy is trying to measure the height of a nearby flagpole using a mirror.
The mirror is 6 m away from the flagpole and 2 m away from sandy.
If sandy is 1.5 m tall how tall is the flagpole?
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

In the Figure below,  AB represents the flagpole;  CD represents Sandy  and  ====  represents the mirror.

The rays of light are shown by points.


According to the optics law  (the reflection law),  angle  AMB  is equal to angle  CMD, 
so the right-angled triangles  AMB  and  CMD  are similar.


From the triangles similarity, we have this proportion  abs%28AB%29%2Fabs%28AM%29 = abs%28CD%29%2Fabs%28MC%29.


Substituting the given values there, we have  x%2F6 = 1.5%2F2, where x is the height of the flagpole.


It gives the solution for the tree's flagpole  x = %286%2A1.5%29%2F2 = 3*1.5 = 4.5 meters.


ANSWER.  The height of the flagpole is 4.5 meters.

Solved. 
                    B
                    +
                    |  .
                    |     .
                    |         .                       D
                    |            .                    o
                    |                .             . _|_
                    |                   .       .   / | \
                    |                      . .        |
                    +---------------------=====------/ \--
                    A                       M         C

                                  F i g u r e

Solved.

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For other similar problem just solved in this site,  see the lesson
    - Using proportions to solve word problems in Geometry
(Problem 1),  with full explanations and illustration.

Learn the subject from there.