Question

The foot of a ladder is 6 m away from its wall and its top reaches a
window 8 m above the ground.
(i) Find the length of the ladder.
(ii) If the same ladder is shifted such that its foot is 8 m away from
the wall, then to what height does its top reach?

Answer 1

The statement forms a right triangle where:

Base, b = 6m

Perpendicular, p= 8m

(i) Length of the ladder, Hypotenuse,

$h = \sqrt{ {b}^{2} + {p}^{2} }$

$= \sqrt{ {(6m)}^{2} + {(8m)}^{2} }$

$= \sqrt{36 {m}^{2} + 64 {m}^{2} }$

$= \sqrt{100 {m}^{2} }$

$= 10m$

(ii) Now, the base is 8m and the perpendicular is unknown. The ladder now will reach the height of,

$p = \sqrt{ {h}^{2} - {b}^{2} }$

$= \sqrt{ {(10m)}^{2} - {(8m)}^{2} }$

$= \sqrt{100 {m}^{2} - 64 {m}^{2} }$

$= \sqrt{36 {m}^{2} }$

$= 6m$