#### A man sees the top of a tower in a mirror which is at a distance of 87.6m from the tower. The 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

Anonymous

0

How tall is the tower

Krishna

0

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}

Step 4: Substitute the known values in the AAA theorem

EXAMPLE: \frac{1.5}{h}=\frac{0.4}{87.6}

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

h = 328.5 m

The height of the lamp post is 328.5 m