Question

The distance between the tips of the poles 10m and 18m high is 17m, then the distance between their foot is​

Answer 1

Refer the attached figure

Height of tower AB = 10 m

Height of tower CD = 15 m

The distance between their feet i.e. BD = 5√3 m

AB = ED = 10 m

CD = CE+ED

15 = CE +10

CE = 15-10 = 5

AE= BD = 5√3 m

In ΔACE

Hypotenuse^2 = Perpendicular^2+Base^2Hypotenuse

2

=Perpendicular

2

+Base

2

AC^2 = CE^2+AE^2AC

2

=CE

2

+AE

2

AC^2 = 5^2+(5\sqrt{3})^2AC

2

=5

2

+(5

3

)

2

AC= \sqrt{5^2+(5\sqrt{3})^2}AC=

5

2

+(5

3

)

2

AC= 10AC=10

Answer 2

Given,

Heights of two poles = 10m and 18m

Distance between their tips = 17m

To find,

The distance between their foot.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

If we visualise the scenario, then we will get that, the upper portion of  8metres (18-10 = 8m) of the higher pole, perpendicular distance between two poles and the distance between their tips, are the height,base and hypotenuse of a right angle triangle, respectively.

Now, we just need to find out the perpendicular distance between them in order to calculate the distance between their foot.

Here, we will be applying Pythagoras theorem,

Let, perpendicular distance between the poles = x metres

So,

(17)² = (8)² + (x)²

289 = 64 + x

x²= 289-64

x² = 225

x = 15

Hence, the distance between their foots is 15 metres.