Question

Two poles stand on the opposite sides of a road, 15m wide. The heights of the two poles are 8m and 9m respectively. Find the distance between their tops, correct upto two decimal places.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

AB and CD be two poles stand on the opposite sides of a road, 15m wide such that A is the base and B is the top of pole AB and C is the base and D is top of second pole and let assume AB = 8 m and CD = 9 m.

So, AC = 15 m

Now, from B, drop BE perpendicular on CD intersecting CD at E.

So, ACEB is a rectangle and

• AB = CE = 8 m

• AC = BE = 15 m

So, DE = CD - CE = 9 - 8 = 1 m

Now, In right angle triangle BDE

Using Pythagoras Theorem, we have

$\rm :\longmapsto\: {BD}^{2} = {DE}^{2} + {BE}^{2}$

$\rm :\longmapsto\: {BD}^{2} = {1}^{2} + {15}^{2}$

$\rm :\longmapsto\: {BD}^{2} =1 + 225$

$\rm :\longmapsto\: {BD}^{2} = 226$

$\rm :\longmapsto\: {BD} = \sqrt{226}$

So, using Long Division Method, we have

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:15.03 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:226.0000 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \:1 \: \: \: \: \: \: \:  \:  \:    \: \:\:}} \\ {\underline{\sf{25}}}& {\sf{\:\: 126 \: \: \: \: \: \: \:   \:\:}} \\{\sf{}}& \underline{\sf{\:\:125 \: \: \: \: \: \: \: \:  \:}} \\ {\underline{\sf{3003}}}& {\sf{\: \: \: \: \: \: 10000 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \:9009\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \: \: \: \: 991\:\:}} \end{array}\end{gathered}\end{gathered}$

Hence,

$\rm :\longmapsto\: {BD} = \sqrt{226} = 15.03 \: m$

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More to know

1. Pythagoras Theorem :-

This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

4. Basic Proportionality Theorem :-

If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.