MCQ
In $\triangle\text{ABC},\text{AB}=6\sqrt{\text{3 cm}}=\text{AC}=12\text{ cm}$ and $\text{BC}=6\text{ cm}$ The angle $B$ is :
- A$120^\circ$
- B$60^\circ$
- ✓$90^\circ$
- D$45^\circ$
✓
Answer
Correct option: C.
$90^\circ$
Given,
In$\triangle\text{ABC},\text{AB}=6\sqrt{\text{3 cm}}=\text{AC}=12\text{ cm}$ and $\text{BC}=6\text{ cm}$
Here, $AC$ is the longest side.
If the square of the hypotenuse is equal to the square of the other two sides,
then it is a right angled triangle.
$\text{So},\text{AC}^2=\text{AB}^2+\text{BC}^2$
$(12)^2=(6\sqrt3)^2+(6)^2$
$144=108+36$
$144=144$
$\therefore\triangle\text{ABC}$ is a right angled triangle and angle opposite to hypotenuse,
i.e. opposite to $AC$ is $\angle\text{b}$ and is equal to $90^\circ$
In$\triangle\text{ABC},\text{AB}=6\sqrt{\text{3 cm}}=\text{AC}=12\text{ cm}$ and $\text{BC}=6\text{ cm}$
Here, $AC$ is the longest side.
If the square of the hypotenuse is equal to the square of the other two sides,
then it is a right angled triangle.
$\text{So},\text{AC}^2=\text{AB}^2+\text{BC}^2$
$(12)^2=(6\sqrt3)^2+(6)^2$
$144=108+36$
$144=144$
$\therefore\triangle\text{ABC}$ is a right angled triangle and angle opposite to hypotenuse,
i.e. opposite to $AC$ is $\angle\text{b}$ and is equal to $90^\circ$
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