Question

9. Two poles 8 m and 16 m high stand up right on the road. If their feet are 15 m apart, find the distance between their tops
​

Answer 1

Step-by-step explanation:

Diagram:- Refer the attachment.

Given:-

• Height of first pole = 8m

• Height of second pole = 16m

• Distance between the feet of poles = 15m

To Find:-

• The distance between the tops of the two poles.

Solution:-

Let the height of the first pole be AB = 8m

And height of the season pole be DC = 16m

• AC = 15m

Let us draw a line BE perpendicular to CD. i.e BE ⊥CD

And, AC ⊥ DC

So, BE = AC = 15m

And, AB = EC = 8m

Now:-

$\sf \implies DE = DC - EC$

$\sf \implies DE = 16 - 8$

$\sf \implies DE = 8m$

$\sf In \: \triangle BED$

By applying Pythagoras Theorem:-

$\sf \implies (Hypotenuse)^2 = (Base)^2 + (Height)^2$

$\sf \implies BD)^2 = DE^2 + (BE)^2$

$\sf \implies BD^2 = (8)^2 + (15)^2$

$\sf \implies BD^2 = 64 + 225$

$\sf \implies BD^2 = 289$

$\sf \implies BD = \implies{289}$

$\sf \implies BD = 17m$

$\underline{\boxed{\therefore \textsf{\textbf{Distance \: between \: their \: tops = 17m}}}}$

Answer 2

Given:-

• Height of two poles = 8m and 16m
• Distance between their feet = 15m

Find:-

• Distance between their tops.

Diagram:-

Let, two poles AB and CD

where, AB = 16m and CD = 8m

Now, Draw CE ⊥ AB

So, EB = CD = 8m, EC = BD = 15m

and, ∠AEC = 90°

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\linethickness{0.4mm}\put(0,0){\line(0,1){6}}\put(0,0){\line(1,0){4}}\put(4,0){\line(0,1){4}}\multiput(0,4)(0.6,0){7}{\qbezier(0,0)(0,0)(0.5,0)}\qbezier(0,6)(0,6)(4,4)\put(-0.5,-0.5){B}\put(-0.5,6){A}\put(-0.5,3.8){E}\put(-0.8,2.9){\bf{16m}}\put(4.3,-0.5){D}\put(4.3,3.8){C}\put(0,2.2){\bf{8m}}\put(0,4){\framebox(0.3,0.3)}\put(4.1,2.2){\bf{8m}}\put(2,-0.3){\bf{15m}}\put(1.5,3.7){\bf{15m}} \end{picture}$

Solution:-

Here,

→ AB = AE + EB

where,

• AB = 16m
• EB = 8m

• Substituting these values •

→ 16 = AE + 8

→ 16 - 8 = AE

→ 8m = AE

→ AE = 8m

Now, In right ∆AEC

↦ H² = P² + B²...........[Pythogoras Theorem]

↦ AC² = AE² + EC²

where,

• AE = 8m
• EC = 15m

• Substituting these values •

➠ AC² = AE² + EC²

➠ AC² = 8² + 15²

➠ AC² = 64 + 225

➠ AC² = 289

➠ AC = √(289)

➠ AC = 17m

∴ AC = 17m

Hence, Distance between the tops of the tower is 17m.