Ex.6.5 Q17 Triangles Solution - NCERT Maths Class 10

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Question

Tick the correct answer and justify : In \(\Delta ABC\), \(AB =\) \(6\sqrt{3}\,\text{cm}\) , \(AC =\) \(12 \;\rm{}cm\) and \(BC =\) \(6 \;\rm{}cm\). The angle \(B\) is

(A) \(120^\circ\) (B) \(60^\circ\) (C) \(90^\circ\) (D) \(45^\circ\)

 

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: ( c)

In \(\Delta ABC\)

\[\begin{align}A B&=6 \sqrt{3} \mathrm{cm} ; A C=12 \mathrm{cm} ; B C=6 \mathrm{cm} \\ A B^{2}&=108 \mathrm{cm}^{2} ; A C^{2}=144 \mathrm{cm}^{2} ; B C^{2}=36 \mathrm{cm}^{2} \\\\ A B^{2}+B C^{2}&=(108+36) \mathrm{cm}^{2} \\ \quad&=144 \mathrm{cm}^{2} \\ \Rightarrow A C^{2}&=A B^{2}+B C^{2}\end{align}\]

Pythagoras theorem is satisfied

\[\Rightarrow \angle ABC={{90}^{0}}\]