Question

A ladder 8.5 m long rests against a vertical wall with its foot 4 m away from the wall. How high up the wall the ladder reaches?

Answer 1

Answer:

length of ladder(L)=8.5m

distance between foot of the ladder and the wall(d)=4m

length of the wall(x)=?

by Pythagoras theorem,

[AC^2=AB^2+BC^2]

(L^2)=(X^2)+(d^2)

(L^2)-(d^2)=x^2

(8.5^2)-(4^2)=x^2

72.25-16=x^2

56.25=x^2

X=√56.25

x=7.5

the ladder reaches 7.5 m on the wall

Answer 2

Concept

Pythagoras theoram states that in a triangle with one angle = 90 degrees,

(Hypotenuse)^2 = (base)^2 + (height)^2

Given

A ladder is 8.5 m long and 4m away from the wall

Find

we need to find how high up the wall the ladder reaches

Solution

Let the length of ladder be x

x = 8.5

Let the distance between foot of the ladder and the wall be y

y = 4

let the length of the wall be z

Since the wall will make an angle of 90 degrees with the land,

by using Pythagoras theorem we get

(x^2)=(y^2)+(z^2)

(x^2) - (y^2)= z^2

(8.5^2)-(4^2)= z^2

72.25 - 16=z^2

56.25 = z^2

z =√56.25

x= 7.5

Thus, the ladder reaches 7.5 m up the wall

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