Gary has a tree that is leaning in his front yard. He is wanting to stake it in the ground to straighten the tree back . The stakes need to be how far away from each other on the ground if the angle around the tree needs to be acute ? Round your answer to the nearest thousandth

They have to be less than 12 feet apart.

Step-by-step explanation:  If the legs of the triangle are the ropes, they would form a right triangle with the imaginary hypotenuse on the ground being the square root of the sums of the squares. 8.5²+ 8.5² = 72.25 + 72.25 or 144.5   very slightly more than 12²  so if the stakes are less than 12 feet apart, the ropes will form an acute angle.

BTW, This will never work as shown in the illustration. No certified arborist would attempt to straighten a tree in these proportions with ropes and stakes.  If a young tree is less than 4 inches in diameter, this might work. The illustration shows a mature-looking tree, probably 50 years old with a diameter of at least 16 inches.