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**Topic**

In the coordinate plane *Oxygen*for triangle *ABC* yes *A*(– 2 ; 4), *REMOVE*(– 5 ; − 1), *OLD*(8 ; – 2). Triangle solver *ABC* (rounding angle measurements to the nearest unit).

**Solution method – See details**

Step 1: Calculate the lengths of the sides *AB*, *AC*, *BC*

Step 2: Use the cosine theorem, the sine theorem to calculate the angle measure

**Detailed explanation**

\(\overrightarrow {AB} = ( – 3; – 5) \Rightarrow AB = \sqrt {34} \);

\(\overrightarrow {AC} = (10; – 6) \Rightarrow AC = 2\sqrt {34} \);

\(\overrightarrow {BC} = (13; – 1) \Rightarrow BC = \sqrt {170} \)

Applying the cosine theorem to triangle ABC we have:

\(\cos A = \frac{{A{B^2} + A{C^2} – B{C^2}}}{{2.AB.AC}} = 0\)\( \Rightarrow \ widehat A = {90^0}\)

\(\cos B = \frac{{A{B^2} + B{C^2} – A{C^2}}}{{2.AB.BC}} = \frac{{\sqrt 5 } }{5}\)\( \Rightarrow \widehat B \approx {63^0}\)

\( \Rightarrow \widehat C = {90^0} – \widehat B \approx {27^0}\)

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