Question

Geometrically, find the value the cos45°

Answer 1

$\frac{1}{ \sqrt{2} }$

Answer 2

Let ΔABC be a right angle Δ with ∠B = 90° and ∠BAC = 45°

∴∠ACB will also be 45°

∵∠BAC = ∠ACB = 45°

∴ AB = BC

Let AB = x

Then BC = x (∵AB = BC)

By Pythagorean Theorem,

AC = √(AB² + BC²)

      = √(x² + x²)  (∵ AB = BC = x)

      =√(2x²)

∴ AC = √2 x

Now we know that cosФ = base/hypotenuse

∴ cos∠BAC = AB/AC

or, cos45° = x/√2 x  (∵ ∠BAC = 45°)

∴ cos45° = 1/√2