Question

What is the value of x in a triangle with the verticies (6,5) (8,2) (x,11) and is 15 square units

Answer 1

Im getting ready to upload a picture, this is not the easiest way, but the fastest way i know of to tackle this problem. it uses vectors and a matrix. If you want i can make another solution using the distance formula and law of sines/cosines/whatever, although it will be a lot longer than my current solution

Answer 2

impress me joe

Answer 3

the idea for this comes from the fact that the det of 2x2 matrix gives you the area of the parallelogram formed by the vectors. the triangle is half that area.

Answer 4

did you try the draw the triangle with vertices (-8,11), (6,5) and (8,2)

Answer 5

hmm...trying to verify the answer and its not working...maybe my idea is a fluke >.< one sec <.<

Answer 6

i think x has to be positive

Answer 7

how is x = -8 in that picture?

Answer 8

satellite!

Answer 9

http://en.wikipedia.org/wiki/Determinant#2-by-2_matrices
check this out, jump to 2x2 matrices part

Answer 10

hello my myininaya.

Answer 11

i got x=11 but i dont know if it is right

Answer 12

it is not 4 or eight

Answer 13

11 is not a option

Answer 14

is it 12? x = 12

Answer 15

do you know the way joe was talking about with matrices?

Answer 16

-8 and 12 works

Answer 17

oh really? sweet :P

Answer 18

so its multiplie choice
of those choices the answer is most likely 12 since i cannot draw a traingle with x=-8

Answer 19

method? or guess and check?

Answer 20

it comes as -8 or 12 as one answer

Answer 21

\[\left| \det(A) \right| = area \]
of the parallelogram, thats what generates 2 answers, i forgot that in my sketch

Answer 22

i forgot the absolute value

Answer 23

nice work

Answer 24

im jealous

Answer 25

gj joe

Answer 26

One of my professors has an extreme passion for all that is Linear Algebra, and it rubbed off on me, so ive been reading books on the subject. its a beatiful subject :)

Answer 27

Thanks so much joe and the other 2 of you :)

Answer 28

satellite and i were just here for looks

Answer 29

i give you medals because you both are awesome :)

Answer 30

how sweet :)