Foot of a 10 m long ladder leaning against a vertical wall 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.
Let AB be a vertical wall and AC = 10 m is a ladder.
The top of the ladder reaches to A and distance of ladder from the base of the wall BC is 6 m.
In right-angled ΔABC,
`AC^2 = AB^2 + BC^2` ......[By pythagoras theorem]
⇒ `(10)^2 = AB^2 + (6)^2`
⇒ `100 = AB^2 + 36`
⇒ `AB^2 = 100 - 36 = 64`
∴ `AB = sqrt(64)` = 8 cm
Hence, the height of the point on the wall where the top of the ladder reaches is 8 cm.
Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
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