Question

plzz tell the solution​

Answer 1

$\sf\large\underline\purple{QuEsTiOn}$

A man sees the top of a tower in a mirror which is at a distance of 87.6 m from the tower. The mirror is on the ground, facing upward. The man is 0.4 m away from the mirror, and the distance of his eye level from the ground is 1.5 m. How tall is the tower?

$\sf\large\underline\red{AnSWEr}$

Let AB and ED be the heights of the man and the tower respectively. Let C be the point of incidence of the tower in the mirror.

In △ABC and △EDC, we have

∠ABC=∠EDC=90°

∠BCA=∠DCE

(angular elevation is same at the same instant. i.e., the angle of incidence and the angle of reflection are same.)

∴△ABC∼△EDC (AA similarity criterion)

Thus,

$\frac{ED}{AB} = \frac{DC}{BC}$

(corresponding sides are proportional)

$ED = \frac{DC}{BC} \times AB$

$\frac{87.6}{0.4} \times 1.5 = 328.5$

Hence, the height of the tower is $\sf\large\underline\green{328.5m}$