Question

find unknown angles and sides of right angled triangle

help me out​

Answer 1

Answer:

In  ΔEFD, ∠ EFD = 90°

Thus by Pythagoras theorem,

ED² = EF² + FD²

ED² = (2√3)² + (2)²

ED² = 4×3 + 4

ED² = 12 + 4

ED² = 16

∴ ED² = 4 cm

Let ∠DEF be θ

sin θ = $\frac{perpendicular}{hypotenuse}$

sin θ = $\frac{2}{4}$

sin θ = $\frac{1}{2}$

sin sin θ = = sin 30°

∴ θ = ∠DEF = 30°

By angle sum property of triangles,

∠EFD + ∠FDE + ∠DEF = 180°

90° + ∠FDE + 30° = 180°

120° + ∠FDE = 180°

∠FDE  = 180° - 120°

∠FDE  = 60°