.
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?
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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 = .
Substituting the given values there, we have = , where x is the height of the flagpole.
It gives the solution for the tree's flagpole x = = 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.