To find the value of x, use the Law of Cosines with the given sides and angle of ABC. Solve the equation derived from setting AC equal to √73 and applying the Law of Cosines to side AC opposite the 60-degree angle.
To find the value of x in triangle ABC where angle ABC = 60 degrees, AB = (x+2), BC = (2x-3), and AC = √73, we can use the Law of Cosines.
The Law of Cosines states that for any triangle with sides a, b, and c, and the angle opposite side c being γ, the following equation holds true: c² = a² + b² - 2ab*cos(γ).
Since we are given that angle ABC = 60 degrees, we set up the equation AC² = AB² + BC² - 2*AB*BC*cos(60 degrees).
Plugging in the values, we have √73² = (x+2)² + (2x-3)² - 2*(x+2)*(2x-3)*½.
Simplifying the equation, we solve for x.
Once we have the value of x, we can then find the lengths of sides AB and BC by substituting x back into their expressions.
The probable question may be:
In triangle ABC, angle ABC=60 degree, AB=(x+2), BC=(2x-3), AC=\sqrt{73}
Help me find value of