Question

In A ABC , LB= 90° and Ac²= 2Bc² then
LA =​

Answer 1

Answer:

The measure of the angle A is 45°.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

In figure,

△ABC is a right-angled triangle.

m∠B = 90°

AC² = 2 BC² - - - [ Given ]

Now, by Pythagoras theorem,

AC² = AB² + BC²

⇒ 2 BC² = AB² + BC² - - - [ From given ]

⇒ BC² + BC² = AB² + BC²

⇒ BC² = AB²

⇒ AB = BC - - - [ Taking square roots ]

∴ △ABC is an isosceles triangle.

∴ ∠A ≅ ∠C

Now, by angle sum property of triangle,

m∠A + m∠B + m∠C = 180°

⇒ m∠A + 90° + m∠A = 180°

⇒ 2 m∠A + 90° = 180°

⇒ 2 m∠A = 180° - 90°

⇒ 2 m∠A = 90°

⇒ m∠A = 90 ÷ 2

⇒ m∠A = 45°

∴ The measure of the angle A is 45°.