Answer:
DE ≈16.1; m∠E ≈ 60.3°; M∠D ≈ 29.7°
Step-by-step explanation:
1) DE
DE² = DF² + EF² = 14² +8² = 196 + 64 = 260
DE =√26 ≈ 16.1
2) m∠E
sin E = DF/DE = 14/16.1 ≈ 0.8682
m∠E = arcsin 0.8682 ≈ 60.3°
3) m∠D
[tex]\begin{array}{rcl}m\angle D + m\angle E + m\angle F & = & 180^{\circ}\\m\angle D + 60.3^{\circ} + 90^{\circ} & = & 180^{\circ}\\m\angle D + 150.3^{\circ} & = & 180^{\circ}\\m\angle D & = & \mathbf{29.7^{\circ}}\\\end{array}[/tex]
