Answer:
The height of the tower = 420.48 meters
Step-by-step explanation:
For better understanding of the solution, see the figure attached below :
Let the height of the tower be x meters
Now, using the laws of reflection : angle of reflection = angle of incidence
Also, both the tower and the tourist are standing parallel to each other
⇒ ∠A = ∠i ( Alternate interior angles are equal)
Similarly, ∠D = ∠r ( Alternate interior angles)
But, ∠i = ∠r
⇒ ∠A = ∠D
Also, the tourist and the tower is perpendicular to the ground surface.
⇒ m∠B = m∠E = 90°
Now, in ΔABC and ΔDEC
∠A = ∠D (Proved above)
m∠B = m∠E = 90°
So, by AA postulate of similarity of triangles, ΔABC ~ ΔDEC
As the sides of similar triangles are proportional to each other
[tex]\frac{AB}{DE}=\frac{BC}{EC}\\\\\implies\frac{1.92}{x}=\frac{0.4}{87.6}\\\\\implies x=\frac{87.6\times 1.92}{0.4}\\\\\bf\implies x = 420.48\textbf{ meters}[/tex]
Hence, The height of the tower = 420.48 meters
