Answer:
Option C is correct.
Ratio of longer leg to hypotenuse is; 
Step-by-step explanation:
This is the special right angle triangle 30°-60°-90° as shown below in the figure.
- The side opposite the 30° angle is always the shortest because 30 degrees is the smallest angle.
- The side opposite the 60° angle will be the longer leg, because 60 degrees is the mid-sized degree angle in this triangle.
- Finally , the side opposite the 90° angle will always be the largest side(Hypotenuse) because 90 degrees is the largest angle.
In 30°−60°−90° right triangle,
- the length of the hypotenuse is twice the length of the shorter leg,also
- the length of the longer leg is
times the length of the shorter leg.
Then:
the sides are in proportion i.e, 
Therefore, the ratio of the length of the longer leg to the length of its hypotenuse is: 
So in the problem, the length of the chord there is the circumference of the tree. So in order to get the diameter of the tree, we must use the formula in getting the circumference of a circle that is stated as follows.
C = 2pi *Radius
so first we need the get the radius of the tree which represent by this formula:
Radius = C /2pi = 8/6.2832 = 1.2732 ft
Diameter = 2*radius = 2 * 1.27 32 = 2.5465 feet
In summary, the diameter of the tree is 2.565 feet.