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T-Ratios of Some Particular Angles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsT-Ratios of Some Particular Angles3 Marks
Question
Evaluate the following:
In the adjoining figure, $\triangle\text{ABC}$ is a right-angled at B and $\angle\text{A}=30^\circ,$ If BC = 6cm.
Find:
  1. AB
  2. AC.
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✓

Answer

From the given right-angled triangle, we have:
$\frac{\text{BC}}{\text{AB}}=\tan30^\circ$
$\Rightarrow\frac{6}{\text{AB}}=\frac{1}{\sqrt{3}}$
$\Rightarrow\text{AB}=6\sqrt{3}\text{cm}$
Also, $\frac{\text{BC}}{\text{AC}}=\sin30^\circ$
$\Rightarrow\frac{6}{\text{AC}}=\frac{1}{2}$
$\Rightarrow\text{AC}=(2\times6)=12\text{cm}$
$\therefore\ \text{AB}=6\sqrt{3}\text{cm}$ and $\text{AC}=12\text{cm}$

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