## Solve Lesson 21 Page 67 Math 10 – Kite >

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:

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

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

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