Q. 1575.0( 4 Votes )

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

Answer :

Given: Height of window = 8m

Distance of ladder to wall = 6m

**Formula Used/Theory:-**

**Pythagoras theorem:-**

Base^{2} + Height^{2} = Hypotenuse^{2}

Height of ladder (Hypotenuse)

Height of wall (Height) = 8m

Distance of wall and foot of ladder = 6m

Base^{2} + Height^{2} = Hypotenuse^{2}

6^{2} + 8^{2} = Hypotenuse^{2}

Hypotenuse^{2} = 36 + 64 = 100

Hypotenuse = √100 = 10m

(i) Height of ladder is 10m

(ii) If ladder is shifted 8m from wall

Then;

Base = 8m

Height of ladder will remain constant(Hypotenuse) = 10m

Distance of wall till ladder reach(Height)

Base^{2} + Height^{2} = Hypotenuse^{2}

8^{2} + Height^{2} = 10^{2}

Height^{2} + 64 = 100

Height^{2} = 100-64 = 36

Height = √36 = 6m

Ladder reach 6m above the ground

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