Foot of a 10 m long ladder leaning against a vertical well is 6 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

Given,

Let PQ be a vertical wall and PR = 10m is a ladder.

The top of the ladder reaches to P and distance of ladder from the base of the wall QR is 6m.

In right angled ∆PQR,

PR² = PQ² + QR² [by Pythagoras theorem]

⇒ (10)² = PQ² + (6)²

⇒ 100 = PQ² + 36

⇒ PQ² = 100 – 36 = 64

∴ PQ = √64 = 8 cm

Hence, the height of the point on the wall where the top of the ladder reaches is 8cm.