Question

Which set of three segments can form a triangle? (12, 30, 5)(32,19,22) (29 35, 6) (16, 31,14)

Answer 1

I was told all of them can form triangle but that's not an option

Answer 2

how are the segments defined?

Answer 3

are those points, or vectors?

Answer 4

if they are vectors, determine their lengths

Answer 5

how can you tell if they make a triangle?

Answer 6

http://learn.flvs.net/webdav/assessment_images/educator_math3/v8/08_TB_01_229.jpg the picture is here

Answer 7

Are these the coordinates in 3-space for the triangle?

Answer 8

@starryknight

Answer 9

\[d=\sqrt{\left( x2-x1 \right)^{2}+\left( y2-y1 \right)^{2}+\left( z2-z1 \right)^{2}}\]

for a triangle sum of any two sides>its third side.
now you can verify.

Answer 10

Assuming those are the coordinates given in 3-space, we can apply the Triangle Inequality to determine whether a third side would satisfy the conditions of forming a triangle. We first choose to random coordinates. I will choose the first two: A(12, 30, 5) and B(32, 19, 22). We need to choose 1 more. I will choose the last set of coordinates; C(16, 31, 14). To figure whether these 3 coordinates will form a triangle, we need to apply the Triangle Inequality:\[\bf |\vec a|+|\vec b| > |\vec a + \vec b|\]What this translates in to is that for any triangle, the sum of any two sides must be greater than the third side. To check whether this is true or not for the triangle with the 3 chosen coordinates, we will computer the magnitude of each side (Note that in 3-space the magnitude of a line going through points \(\bf (a_{1}, b_{1} ,c_{1})\) and \(\bf (a_{2},b_{2},c_{2})\) is given by \(\bf \sqrt{(a_{2}-a_{1})^2+(b_{2}-b_{1})^2+(c_{2}-c_{1})^2}\).)

Let's find side lengths AB, AC, and BC. Using the above formula, we get:\[\bf |\vec {AB}| \approx 28.460\]\[\bf |\vec {AC}|\approx 9.899\]\[\bf |\vec{BC}| \approx 21.541\]Let's see if these side lengths satisfy the Triangle Inequality:\[\bf |\vec{AB}|+|\vec{AC}| > |\vec{BC}| \rightarrow 28.460 + 9.899 > 21.541 \rightarrow 38.359>21.541\]This is obviously not true so the chosen coordinates will not form a triangle. Now repeat the same process with different coordinates until you get a set that works.

@starryknight