Question

In ∆ABC, angle A= 60, angle B = 90, angle C = 30, AB = √3 cm. Then AC = *
1)√3 /2
2)2√3
3)√3
4)1/√3​

Answer 1

Given,

$\[\begin{array}{l}\angle A = 60^\circ \\\angle B = 90^\circ \\\angle C = 30^\circ \\AB = \sqrt 3 cm\\AC = ?\end{array}\]$

Solution,

Use sine law,

$\[\frac{{\sin A}}{{BC}} = \frac{{\sin B}}{{AC}} = \frac{{\sin C}}{{AB}}\]$

$\[\frac{{\sin 90^\circ }}{{AC}} = \frac{{\sin 30^\circ }}{{\sqrt 3 }}\]$

$\[AC = \frac{{\sqrt 3 }}{{\sin 30^\circ }}\]$

$\[AC = 2\sqrt 3 \]$

Hence the value of AC is $\[2\sqrt 3 cm\]$

The correct option is (2), i.e. $\[2\sqrt 3 cm\]$