Question

Before rock climbing, Fernando, who is 5.5 ft tall, wants to know how high he will climb. He places a mirror on the ground and walks six feet backwards until he can see the top of the cliff in the mirror.

If the mirror is 34 feet from the cliff side, determine the height of the cliff.

Answer 1

Explanation:

5.5(34)

187

31.2

​

=

cliff’s dist. to the mirror

cliff’s height

​

=

34

h

​

=6h

=6h

≈h

​

31.2

Answer 2

The height of the cliff is 31.17 feet.

Explanation:

For better understanding of the solution see the attached figure :

Let the height of cliff be x feet.

In ΔABC and ΔDEC,

m∠ABC = m∠DEC = 90° (Angle made between the height and the ground is right angle)

∠ACB = ∠DCE ( Angle of reflection = Angle of incidence because N is normal )

So, By AA postulate of similarity of triangles, ΔABC ~ ΔDEC

Now as triangles are similar, their sides will be proportional to each other.

`(AB)/(DE)=(BC)/(EC)=(AC)/(DC)\\\\Taking,(AB)/(DE)=(BC)/(EC)\\\\\implies (5.5)/(x)=(6)/(34)\\\\\implies x=(34* 5.5)/(6)\\\\\bf\implies x = 31.17`

Hence, The height of the cliff is 31.17 feet