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

Maharashtra BoardEnglish MediumSTD 10MathsTrigonometric Ratios of Some Particular Angles4 Marks
Question
Evaluate the following:
In the adjoining figure, $\triangle\text{ABC}$ is a right-angled at B and $\angle\text{A}=45^\circ,$ If $\text{AC}=3\sqrt{2}\text{cm},$
Find:
  1. BC.
  2. AB.
✓

Answer

From the given right-angled $\triangle\text{ABC},$ we have:
$\frac{\text{BC}}{\text{AC}}=\sin45^\circ$
$\Rightarrow\frac{\text{BC}}{3\sqrt{2}}=\frac{1}{\sqrt{2}}$
$\Rightarrow\text{BC}=3\text{cm}$
Also, $\frac{\text{AB}}{\text{AC}}=\cos45^\circ$
$\Rightarrow\frac{\text{AB}}{3\sqrt{2}}=\frac{1}{\sqrt{2}}$
$\Rightarrow\text{AB}=3\text{cm}$
$\therefore\ \text{BC}=3\text{cm}$ and $\text{AC}=3\text{cm}$

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