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In the adjoining figure, ABC is a right triangle right angled at B. If AB = 10 cm and ∠C = 30°, then the length of the side BC is

  1. 103\dfrac{10}{\sqrt{3}} cm

  2. 10310\sqrt{3} cm

  3. 20 cm

  4. 5 cm

In the figure, ABC is a right triangle right angled at B. If AB = 10 cm and ∠C = 30°, then the length of the side BC is? Trigonometrical Ratios of Standard Angles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Trigonometrical Ratios

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Answer

By formula,

tan C = PerpendicularBase\dfrac{\text{Perpendicular}}{\text{Base}}

⇒tan 30°=ABBC⇒13=10BC⇒BC=103 cm.\Rightarrow \text{tan 30°} = \dfrac{AB}{BC} \\[1em] \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{10}{BC} \\[1em] \Rightarrow BC = 10\sqrt{3} \text{ cm}.

Hence, Option 2 is the correct option.

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