Question

In a triangle ABC , If AB = 8 cm , BC = 5 cm and CA = 9 cm , then the greatest angle is
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Answer 1

Answer:

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Answer 2

Greatest angle in ΔABC is ∠B and about 84.26° where  AB = 8 cm , BC = 5 cm and CA = 9 cm

Given:

• ΔABC
• AB = 8 cm
• BC = 5 cm
• CA = 9 cm

To Find:

• The Greatest angle in the triangle

Solution:

• Angle opposite to largest sides is greatest in a given Triangle

Step 1:

Compare given sides of triangle

9 > 8 > 5

Hence

CA > AB > BC

Step 2:

Check the angle opposite to greatest side CA

Angle B is opposite to CA

Hence Angle B is greatest

Additional Info:

Find Measure of angle B using cosine rule

CA² = AB² + BC²  - 2AB.BC cos∠B

9² = 8² + 5² - 2(8)(5)cos∠B

=> 81 = 64 + 25 - 80cos∠B

=> -8 = -80cos∠B

=> cos∠B = 1/10

=> ∠B ≈  84.26°