Question

In ∆ABC,B=90°,A=30°,AC=14,then find AB and BC

Answer 1

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Answer 2

Triangle

In ΔABC,

$\angle A= 30\textdegree\\ \angle B= 90\textdegree$

$AC= 14\ unit$

According to angle sum property of triangle , sum of all the angles of a triangle is 180°.

In ΔABC,

$\angle A +\angle B +\angle C =180\textdegree\\\implies 30\textdegree+90\textdegree+\angle C=180\textdegree\\\implies \angle C=180\textdegree-(30\textdegree+90\textdegree)\\\implies \angle C =60\textdegree$

Using trigonometric ratios,

$\sin A=\frac{BC}{AC} \\\\\implies sin \ 30\textdegree=\frac{BC}{14} \\ \\\implies \frac{1}{2}= \frac{BC}{14} \\\\\implies BC =7 \ unit$

$\sin AC=\frac{AB}{AC} \\\\\implies sin \ 60\textdegree=\frac{AB}{14} \\ \\\implies \frac{\sqrt{3} }{2}= \frac{AB}{14} \\\\\implies BC =7\sqrt{3} \ unit=12.12 \ unit$

Hence AB is 7 and BC is 7√3 .