Answer:
DE ≈ 40
Step-by-step explanation:
Using the Sine rule in Δ DEF
∠ D = 180° - (58 + 87)° ← sum of angles in a triangle
∠ D = 180° - 145° = 35° , then
[tex]\frac{DE}{sin87}[/tex] = [tex]\frac{EF}{sin35}[/tex] = [tex]\frac{23}{sin35}[/tex] ( cross- multiply )
DE × sin35° = 23 × sin87° ( divide both sides by sin35° )
DE = [tex]\frac{23sin87}{sin35}[/tex] ≈ 40 units ( to the nearest whole number )
