Construct triangle ABC with vertices A(-4,2), B(4,3), C(1,-3). list the angles in?

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Construct triangle ABC with vertices A(-4,2), B(4,3), C(1,-3). list the angles in?
To work out an angle construct the two vectors to that angle and take the dot product.





AB = %26lt;B - A%26gt; = %26lt;4+4, 3-2%26gt; = %26lt;8, 1%26gt;


AC = %26lt;C - A%26gt; = %26lt;1+4, -3-2%26gt; = %26lt;5, -5%26gt;





|| AB || = √(8² + 1²) = √(64 + 1) = √65


|| AC || = √[5² + (-5)²] = √(25 + 25) = √50 = 5√2





AB • AC = %26lt;8, 1%26gt; • %26lt;5, -5%26gt; = 40 - 5 = 35





Angle A can be expressed in terms of the dot product as:





cosA = (AB • AC) / {|| AB || || AC || = 35 / [(√65)(5√2)]


cosA = 7 / [(√65)(√2)] = 7 / √130





A = arccos(7 / √130 ) ≈ 52.1°





The other angles are similarly calculated.
Reply:I'm assuming you want to know angles CAB, ABC, and BCA.


It's an Isocoles triangle, so base angles(CAB,ABC) are equal.





CAB and ABC- 52 Degrees


BCA- 76 Degrees