Krishna
0

Step 1: Understand the question and note down the given data

            From the figure:

            Person's height AB = 1.65 m

            The length of a person's shadow BC = 1. 8 m

            The length of a lamp-post's shadow QR = 5.4 m

            Lamp-post's height PQ = ?

            

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

            From the figure we get

             \angle B = \angle Q = 90 \degree

             \angle C = \angle R, \angle A = \angle P

            Because, AC || PR, all sun’s rays are parallel at any instance)

            We understand the triangles are similar because all three corresponding angles are equal.

            Thus,  ∆ABC ~ ∆PQR ( by AAA Theorem)


Step 3: Calculating unknown length

            The three pairs of corresponding sides are in the same proportion to each other since the triangles are similar.

                    \frac{AB}{PQ} = \frac{BC}{QR}

            Substitute the known values in the above equation

                     \frac{1.65}{PQ} = \frac{1.8}{5.4}

                     PQ = \frac{5.4 * 1.65}{1.8}

                     PQ = 4.95 m

             Hence, the height of the lamp post is 4.95 m