Question

f the largest angle of a triangle is 120° and it is included between sides of 1.5 and 0.5, then (to the nearest tenth) the largest side of the triangle is (Blank) how do i figure this out?

Answer 1

ok this is basically like area.

Answer 2

in all honesty, the assignment i was needing help with this for just crashed, and i cant even get beck in to it

Answer 3

so it shows you have 1.5 and0.5 and there asking for the largest side. what im confused about is how... oh nvm

Answer 4

well its great to know this stuff anyways,

Answer 5

i guess what im seeing is the the degree is 120 inside of each side so you have two sides 0.5 and 1.5 you now need to find largest side. How do you think we should go about finding this?

Answer 6

Let's tackle this problem with a more generalized problem, say we have for instance, the angle \(\angle \beta \) and the two adyacent sides of the angle as given information, of course we will name them "a" and "b", now let's imagine for a second that "c" is the side opposite to angle \(\angle \beta \) so we will name the triangle as:

So, we will define "h" as the heigth of this triangle, which will imply that it is perpendicular to segment "b".
This will define two right angle triangle which we can apply pythagorean theorem with, ending up with:
\[\triangle AB(h) \iff a^2=h^2+u^2\]
\[\triangle CB(h) \iff c^2=h^2+(b-u)^2\]
Therefore, by combining both equations:
\[c^2=(a^2-u^2)+(b^2-2bu+u^2)\]
\[c^2=a^2+b^2-2bu\]
By definition, u should be able to be calculated by cosine:
\[\cos \beta = \frac{ u }{ a }\]
\[u=\cos \beta.a\]
And replacing it on the equation of "c":'
\[c^2=a^2+b^2-2ab. \cos \beta\]
And this last equation is called the "Cosine theorem", which allows us to calculate any side of any triangle as long as we have two sides and the angle between them.