Some questions and their alternative answers are given. Select th… - Vidyadip

MCQ

Some questions and their alternative answers are given. Select the correct alternative.
In D ABC, AB = $6\sqrt 3$ cm, AC = 12 cm, BC = 6 cm. Find measure of $\angle A$.

✓
$30^\circ$
B
$60^\circ$
C
$90^\circ$
D
$45^\circ$

✓

Answer

Correct option: A.

$30^\circ$

As,

$(6 \sqrt{ }3)^2+6^2=12^2$
$\Rightarrow A B^2+B C^2=A C^2$
i.e. sides of the triangle $A B C$ satisfy the Pythagoras theorem
$(\text { Hypotenuse })^2=(\text { base })^2+(\text { Perpendicular })^2$
$\therefore \mathrm{ABC}$ is a right-angled triangle with hypotenuse as AC
Now,
$B C=\frac{1}{2} A C$
By converse of $30^{\circ}-60^{\circ}-90^{\circ}$ triangle theorem i.e.
In a right-angled triangle, if one side is half of the hypotenuse then the angle opposite to that side is $30^{\circ}$.
$\angle A=30^{\circ}$

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