Question

A boy 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?

Answer 1

The house is 12 feet tall.

Answer 2

The height of the building = 12 feet

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

`\implies (CA)/(DE)=(AB)/(EB)\\\\\implies (6)/(DE)=(8)/(16)\\\\\implies DE=12`

Hence, The height of the building = 12 feet