Ex.6.5 Q10 Triangles Solution - NCERT Maths Class 10

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Question

A guy wire attached to a vertical pole of height \(18\)\(\rm{}m\) is \(24\) \(\rm{}m\) long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

Diagram

Text Solution

Reasoning:

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Steps:

\(AB\) is the length of the pole = \(18\)\(\rm{}m\)

\(AC\) is the length of the guy wire = \(24\)\(\rm{}m\)

\(BC\) is the distance of the stake from the pole \(= ?\)

In\(\Delta ABC\,\,\,\,\,\angle ABC={{90}^{0}}\)

\[\begin{align} B C^{2} &=A C^{2}-A B^{2} \text { (Pythagoras theorem) } \\ B C^{2}&=24^{2}-18^{2} \\ B C^{2}&=576-324 \\ B C^{2}&=252 \\ B C &=2 \times 3 \sqrt{7} \\ B C &=6 \sqrt{7} \end{align}\]

The distance of the stake from the pole \(=6\sqrt{7}\rm{}m\)