Clearly, Δ ABC and Δ ABD are right angled triangles

where AD = 10cm BC = CD = 4cm

BD = BC + CD = 8cm

Applying Pythagoras theorem, (hypotenuse)² = (perpendicular)² + (base)²

∴AD² = BD² + AB²

= (10)² = (8)² + AB²

= 100 = 64 + AB²

= AB² = 36

= (6)²

→ AB = 6cm

Now applying Pythagoras theorem, (hypotenuse)² = (perpendicular)² + (base)²

∴AC² = BC² + AB²

= AC² = (4)² + (6)²

= AC² = 16 + 36

= 52

→ AC = √52

= 2√13cm

i. sinθ = BC/AC =

= 2/√13

= (2√13)/13

ii. cosθ = AB/AC =

= 3/√13

= (3√13)/13