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6 July, 01:44

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

m∠DEF?

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Answers (1)
  1. 6 July, 01:50
    0
    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
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