Question

find the measure of all angles of triangle KLM for K(-2,1), L(3,2), and M(1,-3)

Answer 1

Okay, I just made a graphic

Answer 2

I converted the points into vectors
vector KL=(5) LM=(-2) km=(3)
(1) (-5) (-4)

Answer 3

am I wrong in assuming this is for trig?

Answer 4

I'm not very familiar with those kind of vectors. I'm used to dealing with vectors in physics 45° mag 20 - that kind of thing
This is definitely trig

Answer 5

Line KL² = 5² + 1² = 26
Line KL = sqrt(26) = 5.099019
I could figure out the othe sides and then the angles but I was wondering if there's an easier way to do this.

Answer 6

heheh, I wasn't thinking on using vectors, I was thinking on using the distance formula to get the sides length and then use the cosines rule

Answer 7

Well okay, I was going to find the other 2 sides and then use the trig.

Answer 8

Line KM² = 3² + 4²
Line KM² = 25
Line KM = 5

Answer 9

Line LM² = 5² + 2²
Line LM² = 29
Line LM = 5.38516

Answer 10

Angle KML = arcsine (3/5) PLUS arcsine(2/5.38516)
= 36.87° + 21.801° = 58.671°

Answer 11

Angle KLM = 90° -[arcsine(2/5.38516) + arcsine(1/5.0990919)]
Angle KLM = 90° - [21.801° + 11.31°]
Angle KLM = 56.889°

Answer 12

Angle LKM = arcsine (1/5.0990919) PLUS arcsine (4/5) =
11.31° + 53.13° = 64.44°

And the angles all sum to 180°