need help with this i have to calculate the leng of one side?

Question

of a triangle that is oposite to a 120° angle, the other 2 sides are R and 2R

i know all the trigs formulas, but i cant tell wich is the adyacent or the hipotenuse or what?

i know all the trigs formulas, but i cant tell wich is the adyacent or the hypotenuse or what?

thank you all, cos law really save me, i need to do lots of this calculations so what i really needed was the way to do it.

Answer 1

You can directly use the trig functions ONLY if it's a right triangle. Your triangle isn't a right triangle, so you have to use the Law of Cosines.

if a, b, c are sides and C is the angle opposite of side c:

c^2=a^2+b^2-2ab(cosC)

As you can see, this is similar to the Pythagorean theorum. In fact, the Pythagorean theorum is just a special case of the Law of Cosines when cosC=0, so c^2=a^2+b^2.

Anyway, your angle is C, your two sides are 1 and 2 units long (ignore the R for now) and little c is the side you're trying to find. Plug away.

Answer 2

Let's think about this:
The angle is 120º and the sides are r and 2r. Prolongue the side that is r and create a straight line. The 2r side will form an angle of 60º with the straight line. Applying a bit of trigonometry, the extended piece will be r, and the side opposite to the 60º angle will be (3^0.5)*r
Applying Pythagoras:
(2r)^2 + ((3^0.5)r)^2=X^2, where X is the unknown side you want to find
4r^2 + 3r^2 = X^2
7r^2 = X2
X = (7^0.5)*r or square root of 7 times r

Answer 3

let a = side R
let b = side 2R
let angle C = 120 degreees

Then use the law of cosines to solve problem:

c^2 = a^2 + b^2 - 2ab cosC
c^2 = R^2 +(2R)^2 - 2(R)(2R) cos 120
c^2 = 5R^2 - 4R^2 (-.500)
C^2 = 3R^2
C = R sqrt(3)

Answer 4

uhm i think in order to get one of the sides, you would have to use one of the angles that is not the 120 one, because side opposite 120 is technically the hypotenuse because it is the longest side, so i would suggest that you use one of the other smaller angles and use SOHCAHTOA to solve the problem

Answer 5

cosine 120=adj/hyp