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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
In $\triangle\text{ABC, }\text{AB}=6\sqrt{3 }\text{ cm},\text{AC}=12\text{ cm}$ and $\text{BC}=6\text{ cm}.$ Then, $\angle\text{B}$ is :
  • A
    $45^\circ$
  • B
    $60^\circ$
  • ✓
    $90^\circ$
  • D
    $120^\circ$
✓

Answer

Correct option: C.
$90^\circ$
In $\triangle\text{ABC},$
$\text{AB}=6\sqrt{3 }\text{ cm},\text{AC}=12\text{ cm}$ and $\text{BC}=6\text{ cm}$
$\text{AB}^2+\text{BC}^2=3\sqrt{3}^2+6^2$
$=108+36=144$
$\text{AC}^2=12^2=144$
$\Rightarrow\text{AB}^2+\text{BC}^2=\text{AC}^2$
So, by the Converse of Pythagoras theorem,
$\triangle\text{ABC}$ is a right angled triangle and since $AC$ is the hypotenuse,
$\angle\text{B}$ which is opposite $\text{AC} = 90^\circ.$

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