Question

A man sees the top of a tower in a mirror which is at a distance of 87.6m from the tower.Yhe mirror is on the ground facing upwards.The man is 0.4m away from the mirror and his height is 1.5m.How tall is the tower? ​

Answer 1

Answer:

Step 1: Examine the given figure and make a note of the given measurements

Step 2: Prove that the two triangles are similar by using the given data.

             EXPLANATION: From the figure we get

                     \angle ∠ B = \angle ∠ D = 90 \degree °

                     \angle ∠ BCA = \angle ∠ DCE

             Because, angle of incidence and angle of reflection are same)

             So, ∆ABC ~ ∆EDC ( by AAA Theorem)

                  

Step 3: Use the AAA theorem to calculate unknown value

        AAA THEOREM: In two triangles, if the angles are equal, then the sides

        opposite to the equal angles are in the same ratio (or proportional) and hence

        the two triangles are similar. 

                  \frac{AB}{ED}=\frac{BC}{CD}EDAB=CDBC

Step 4: Substitute the known values in the AAA theorem

                  EXAMPLE:  \frac{1.5}{h}=\frac{0.4}{87.6}h1.5=87.60.4

                                      h=\frac{1.5*87.6}{0.4}h=0.41.5∗87.6

                                       h = 328.5 m

                          The height of the lamp post is 328.5 m

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