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Mathematics

In the given triangle, the length of AB is :

  1. 424{\sqrt2}

  2. 4 m

  3. 8 m

  4. 6 m

In the given triangle, the length of AB is : Solution of Right Triangles, Concise Mathematics Solutions ICSE Class 9.

Trigonometric Identities

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Answer

Let ∠BAC be x.

Using the angle sum property of a triangle, which states that the sum of all angles in a triangle is 180°:

⇒ ∠BAC + ∠BCA + ∠ABC = 180°

⇒ x + 45° + 90° = 180°

⇒ x + 135° = 180°

⇒ x = 180° - 135°

⇒ x = 45°

Thus, ∠BAC = ∠BCA = 45°. Therefore, Δ ABC is an isosceles triangle, meaning AB = BC = 8 m.

Hence, option 3 is the correct option.

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