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Topic
In the coordinate plane Oxygenfor 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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