(Q18) Two poles of heights 6 m and 11m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.

Solution :

ABCDE5 cm6 cm6 cm11 cm12 cm

Let the height of the first pole AB = m.

Let the height of the second pole CD = m.

Distance between the poles AC = m.

From the figure □ACEB is a rectangle.

∴ AB = CE = 6 m

ED = CD - CE = - = m

Now in ∆BED; ∠E = 90°; DE = 5 m; BE = 12 m

BD2 = BE2 + DE2

[hypotenuse2 = side2 + side2 --> Pythagoras theorem]

= 2 + 2 = +

BD2 =

BD = √169 = m

∴ Distance between the tops of the poles = 13 m.