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Trigonometric Ratios of Some Particular Angles — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsTrigonometric Ratios of Some Particular Angles4 Marks
Question
Evaluate the following:
In the adjoining figure, $\triangle\text{ABC}$ is a right-angled triangle in which $\angle\text{B}=90^\circ,\angle\text{A}=30^\circ$ and $AC = 20\ cm.$
Find:
  1. $BC$
  2. $AB.$
✓

Answer

From the given right-angled triangle, we have:
$\frac{\text{BC}}{\text{AC}}=\sin30^\circ$
$\Rightarrow\frac{\text{BC}}{20}=\frac12$
$\Rightarrow\text{BC}=\frac{20}{2}=10\text{cm}$
Also, $\frac{\text{AB}}{\text{AC}}=\cos30^\circ$
$\Rightarrow\frac{\text{AB}}{20}=\frac{\sqrt{3}}{2}$
$\Rightarrow\text{AB}=\Big(20\times\frac{\sqrt{3}}{2}\Big)=10\sqrt{3}\text{cm}$
$\therefore\ \text{BC}=10\text{cm}$ and $\text{AB}=10\sqrt{3}\text{cm}$

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