Answer:
The height of the building = 12 feet
Step-by-step explanation:
Given : AC = 6 feet, AB = 8 feet, BE = 16 feet
To find : Height of the house, DE
Solution : Since the height of both boy and the house are perpendicular to the surface of the ground
⇒ ∠CAB = ∠DEB = 90°
Now, using laws of reflection : angle of incidence = angle of reflection
So, using this condition, it can be concluded that ∠ACB = ∠EDB
Now, In ΔCAB and ΔDEB
∠CAB = ∠DEB = 90° ( Proved above)
∠ACB = ∠EDB ( Proved above)
By AA postulate of similarity of triangles ΔCAB ~ ΔDEB
Now, the sides of similar triangles are proportional to each other
[tex]\implies \frac{CA}{DE}=\frac{AB}{EB}\\\\\implies \frac{6}{DE}=\frac{8}{16}\\\\\implies DE=12[/tex]
Hence, The height of the building = 12 feet
