Step-by-step explanation:

Given:-

Two poles of height 5 m and 8 m stand UPRIGHT in a PLANE ground.

To find:-

If the DISTANCE between their feet is 4 m. find the distance between their tops.

Solution:-

Heights of the two poles = 5m and 8m

Distance between their frets = 4m

Converting the given data into PICTORIAL diagram

(See the above attachment)

Heights of the two poles AB = 5m and CE = 8m

Join A and D

Distance between their FEETS = BC = 4m

=>BC = AD = 4m

CE=ED+CD

=>ED = CE-CD

=>ED = 8-5

Therefore,ED = 3 m

Distance between their tops = AE

In ∆ADE , angle D = 90°

It is a right angled triangle

By Pythagoras theorem

"In a right angled triangle , The square of the hypotenuse is equal to the sum of the squares of the other two sides".

=>AE^2 = AD^2 +ED^2

=>AE^2 = 4^2 + 3^2

=>AE^2 = 16+9

=>AE^2 = 25

=>AE = √25

=>AE = 5 m

Therefore,required distance = 5m

Answer:-

The distance between their tops = 5m

Used formulae:-

Pythagoras Theorem:-

"In a right angled triangle , The square of the hypotenuse is equal to the sum of the squares of the other two sides".