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In △ABC, ∠A = 30° and ∠B = 90°. If AC = 8 cm, then its area is

  1. 16316\sqrt{3} cm2

  2. 16 cm2

  3. 838\sqrt{3} cm2

  4. 636\sqrt{3} cm2

Heights & Distances

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Answer

Considering right angled △ABC we get,

In △ABC, ∠A = 30° and ∠B = 90°. If AC = 8 cm, then its area is. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

⇒sin 30°=BCAC⇒12=BC8⇒BC=4 cm\Rightarrow \text{sin 30°} = \dfrac{BC}{AC} \\[1em] \Rightarrow \dfrac{1}{2} = \dfrac{BC}{8} \\[1em] \Rightarrow BC = 4 \text{ cm}

Similarly,

⇒cos 30°=ABAC⇒32=AB8⇒AB=43 cm\Rightarrow \text{cos 30°} = \dfrac{AB}{AC} \\[1em] \Rightarrow \dfrac{\sqrt{3}}{2} = \dfrac{AB}{8} \\[1em] \Rightarrow AB = 4\sqrt{3} \text{ cm}

Area of right angle triangle = A

∴A=12× base× height⇒A=12×43×4⇒A=83 cm2\therefore A = \dfrac{1}{2} \times \text{ base} \times \text{ height} \\[1em] \Rightarrow A = \dfrac{1}{2} \times 4\sqrt{3} \times 4 \\[1em] \Rightarrow A = 8\sqrt{3}\text{ cm}^2

Hence, Option 3 is the correct option.

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