Question

suppose a triangle has two sides of length 2 and 5 and that the angle between these two sides is 60 degrees. whart is the length of the third side of the triangle

Answer 1

Explanation:

the other answer is correct but missed a few steps in the explanation. so, just to be sure :

yes, we use the law of cosine (or I call it the general Pythagoras for non-right-angled triangles) :

c is the side opposite of the given angle. a, b are the other 2 sides.

c² = a² + b² - 2ab×cos(angle)

in our case

c² = 2² + 5² - 2×2×5×cos(60°) =

= 4 + 25 - 20×0.5 = 29 - 10 = 19

c (the third side) = sqrt(19) = 4.358898944... units

you see how this is connected to the regular Pythagoras in right-angled triangles ?

c² = a² + b² - 2ab×cos(90°)

cos(90°) = 0

and so all that is left is

c² = a² + b²

Answer 2

Explanation:

Using Law of Cosine

Suppose Angle A is 60 degrees which is between sides b and c.

we need to find the length of side a

a^2 = b^ + c^ - 2bcCos60

a^2 = 4 + 25 - 20Cos60

a^2 = 29 - 20Cos60

a = 4.3588