Answer:
Kind of long:
Explanation:
Cosine law is kinda like Pythagorean theorem except the cosine law works for any triangle ....it doesn't have to be a right triangle
Here it is :
c^2 = a^2 + b^2 - 2* a * b cos (angle)
For this triangle c = sqrt(129) a = (x+2) b = (2x+1) angle = 60°
so to find 'x' you'll have to do the following calculations and solve for 'x'
(
)^2 = (x+2)^2 + (2x+1)^2 - 2 ( x+2)(2x+1) cos (60°)
a bit of 'busy work' ...but here it goes: NOTE: (2 * cos 60° = 1 )
129 = x^2 +4x +4 + 4x^2 +4x+1 - (2x^2 +5x+2 ) simplify this to :
129 = 3x^2 + 3x +3 re-arrange to
0 = 3x^2 + 3x - 126 Quadratic formula shows x = 6 or -7 (throw out)