D (5, 7), E (4, 3), and F (8, 2) form the vertices of a triangle. What is

m∠DEF?

DE = √ (1 + 16) = √17

DF = √ (9 + 25) = √34

EF = √ (16 + 1) = √17

The Cosine Law:

(√34) ² = (√17) ² + (√17) ³ - 2 * √17 * √17 cos α

34 = 17 + 17 - 34 cos α

- 34 cos α = 0

cos α = 0

α = 90°

Answer:

m∠DEF = 90° = π/2