Question

In a right angled triangle , if two acute angles are in the ratio 2 : 7 , then find the measures of its acute angles

Answer 1

Step-by-step explanation:

By angle sum property, ∠A+∠B+∠C=180

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Given that △ABC is rightangled at A

∴∠A=90

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∴∠B+∠C=180

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−∠A=180

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−90

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=90

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Given that ∠B:∠C=2:3

Let ∠B=2x and ∠C=3x

⇒2x+3x=90

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⇒5x=90

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⇒x=

5

90

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=18

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∴∠B=2×18

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=36

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and ∠C=3×18

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=54

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Hence the other two acute angles are 36

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and 54

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