Aboy is 6 ft. tall. the distance from the boy to a mirror is 8 ft. from the mirror to the house is 16 ft. how high is the top of the house?

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

Hence, The height of the building = 12 feet