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Question Bank - P2 — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsQuestion Bank - P22 Marks
Question
From given figure, In ∆ABC, If AC = 12 cm. then AB =?

Activity: From given figure, In $\triangle ABC , \angle ABC =90^{\circ}, \angle ACB =30^{\circ}$
$\therefore \angle BAC =\square$
$\therefore \triangle ABC$ is $30^{\circ}-60^{\circ}-90^{\circ}$ triangle
$\therefore$ In $\triangle ABC$ by property of $30^{\circ}-60^{\circ}-90^{\circ}$ triangle.
$ \therefore A B=\frac{1}{2} A C \text { and } \square=\frac{\sqrt{3}}{2} A C$
$\therefore \square=\frac{1}{2} \times 12 \text { and } B C=\frac{\sqrt{3}}{2} \times 12$
$\therefore \square=6 \text { and } B C=6 \sqrt{3} $
✓

Answer

From given figure, in $\triangle ABC , \angle ABC =90^{\circ}, \angle ACB =30^{\circ}$
$\therefore \angle BAC =60^{\circ}$
[Remaining angle of a triangle]
$\therefore \triangle ABC$ is $30^{\circ}-60^{\circ}-90^{\circ}$ triangle.
$\therefore$ In $\triangle ABC$,
by property of $30^{\circ}-60^{\circ}-90^{\circ}$ triangle.
$\therefore AB =\frac{1}{2} AC$
[Side opposite to $30^{\circ}$ ]
and $B C =\frac{\sqrt{3}}{2} AC$
[Side opposite to $60^{\circ}$ ]
$\therefore AB =\frac{1}{2} \times 12$ and $BC =\frac{\sqrt{3}}{2} \times 12$
$\therefore AB =6$ and $BC =6 \sqrt{3}$

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