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30 September, 19:21

Select the correct answer from each drop-down menu. ∆ABC has A (-3, 6), B (2, 1), and C (9, 5) as its vertices. The length of side AB is units. The length of side BC is units. The length of side AC is units. ∠ABC ≈ °.

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  1. 30 September, 20:02
    0
    √50

    √65

    √145

    105 °

    Step-by-step explanation:

    Given the coordinates

    A (-3, 6)

    B (2, 1)

    C (9, 5)

    To find the length of AB, AC and BC, we will use distance formula

    √ ((x2-x1) ² + (y2-y1) ²)

    AB:

    √ (2+3) ² + (1-6) ²

    √5²+5²

    √50

    BC:

    √ (9-2) ² + (5-1) ²

    √7² + 4²

    √49+16

    √65

    AC:

    √ (9+3) ² + (5-6) ²

    √12²+1²

    √145

    To find ∠ABC

    cos (B) = c² + a² - b² / 2ca

    = 65 + 50 - 145 / 2 (√65) (√50)

    cosB = - 0.26311

    B = cos^-1 (-0.26311)

    = 105 °
  2. 30 September, 20:52
    0
    √50

    √65

    √145

    105 °
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