Question

Two poles of height 4m and 9m stand on a plane ground.if the distance between the feet of the poles is 12mt,find the distance between their tops

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Answer 1

⋆ DIAGRAM :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\linethickness{0.5mm}\qbezier(1, 0)(1,0)(1,3)\qbezier(0.99, 3)(4,5)(6,6)\qbezier(6, 0)(6,0)(6,6)\qbezier(6,0)(6,0)(6,3)\qbezier(1,3)(1,3)(6,3)\qbezier(1,0)(11,0)(1,0)\put(5.7,3){\line(0,3){0.3}}\put(5.7,3.3){\line(1,0){0.3}}\put(7.2,3){ \textit{9} m}\put(0.6,-0.2){ \sf P }\put(6.1,-0.2){ \sf Q }\put(6.1,6.2){ \sf T }\put( - 0.9, 1.5){ \textit{4}m}\put( 3, - 0.3){ \textit{12}m}\put(6.1,3){ \sf R }\put(0.6,3){ \sf S }\put(7,3){\vector(0,2){3}}\put(7,3){\vector(0, - 2){3}}\put(0,1){\vector(0,2){2}}\put(0,2){\vector(0, - 2){2}}\end{picture}$

Given Parameters: Two poles of height 4m and 9m stand on a plane ground.if the distance between the feet of the poles is 12m.

Unknown : The Distance between their tops (ST)

Construction : SR ⏊ QR

Answer:

• PS = 4 m
• QT = 9 m
• PQ = 12 m = SR ......[Formed ▭ SRQP]
• RT = QT - RQ = 9 - 4 = 5 m

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle :]

By above definition for right angled triangle TRS,

In ∆TRS where ∠R = 90°

$\sf => (ST)^2 = (SR)^2 + (RT)^2$

$\sf => (ST)^2 = (12)^2 + (5)^2$

$\sf => (ST)^2 = 144 + 25$

$\sf => (ST)^2 = 169$

• Taking square roots on both sides we get :]

$\sf => ST = \sqrt{169}$

$=> \textsf{\textbf{ST = 13 m}}$

Therefore, The Distance between their tops (ST) is 13 m.

Answer 2

GIVEN

• Two poles of height 4 m and 9 m stand on a plane ground. • Distance between the feet of the poles is 12 m.

TO FIND:

• The distance between their tops , DE.

CONSTRUCTION :

• Draw DCI BC.

SOLUTION:

As we know that,

» AB = DC = 12 m.

» AD = BC = 4 m.

* Length of EC,

» EC = BE - BC

» EC = 9 m 4 m.

* Now in A ECD By Pythagoras theorem,

(DE)² = (DC)² + (CE)²

(DE)² = (12) + (5)²

(DE)² = 144 + 25

(DE)² = 169

DE = V169

DE = 13 m.

HENCE THE DISTANCE BETWEEN THE TOP OF THE POLES IS 13 M