Let's rewrite the equation as
This should be enough to convince you that the equation has no solutions, no matter which value for k you choose. In fact, the left hand side of the equation is an absolute value, which by definition is always positive, or zero in the worst case.
The equality asks for this quantity to equal -3, a negative number.
A non-negative quantity can never equal a stricktly negative quantity, so the equation has no solutions.
For the given triangle, the cosine of angle A equals .
Step-by-step explanation:
Step 1; In the given triangle, the opposite side has a length of 9 units, the adjacent side has a length of 3√3 units while the hypotenuse of the triangle measures 6√3 units. To calculate the cosine of angle A we divide the adjacent side by the hypotenuse side.
cos A = .
Step 2; Length of the adjacent side = 3√3 units.
Length of the hypotenuse side = 6√3 units.
cos A = 3√3 / 6√3
cos A = .
To check we also have A = 60° and cos 60° = .
