SOLUTION: Sid wants to find the height of a tree without having to climb it, but it is a cloudy day, so he cannot use shadows. He takes a mirror from his pocket and places it on the ground

Question 1195112: Sid wants to find the height of a tree without having to climb it, but it is a cloudy day, so he cannot use
shadows. He takes a mirror from his pocket and places it on the ground 7.2 m from the base of the
tree. He backs up until he can see the top of the tree in the mirror, a distance of 1.2 m from the mirror.
If Sid's eyes are 1.5 m above the ground, what is the height of the tree?
Answer by ikleyn(52835) (Show Source): You can put this solution on YOUR website!
.
Sid wants to find the height of a tree without having to climb it, but it is a cloudy day,
so he cannot use shadows. He takes a mirror from his pocket and places it on the ground
7.2 m from the base of the tree. He backs up until he can see the top of the tree in the mirror,
a distance of 1.2 m from the mirror.
If Sid's eyes are 1.5 m above the ground, what is the height of the tree?
~~~~~~~~~~~~~~~~~

Solution

In the Figure below,  AB represents the tree;  CD represents Sid  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   = .


Substituting the given values there, we have   = , where x is the height of the tree.


It gives the solution for the tree's height  x =  = 6*1.5 = 9 meters.


ANSWER.  The height of the tree is 9 meters.

Solved.

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

                                  F i g u r e

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