Question

Solve the right triangle. Round decimal answers to the nearest tenth.
​

Answer 1

DE = sqrt(8^2+14^2) = ~16.1

E = arctan(14/8) = 60.3

D= arctan(8/14) =29.7

Explanation:

Answer 2

DE ≈16.1; m∠E ≈ 60.3°; M∠D ≈ 29.7°

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

`\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}`