Answer:
[tex]346.4\text{ ft}[/tex]
Step-by-step explanation:
In all 30-60-90 triangles, the side lengths are in a ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse of the triangle and [tex]x[/tex] is the side opposite to the 30 degree angle.
In [tex]\triangle ABD[/tex], the side marked as 300 ft, AB, is the side opposite to the 30 degree angle. Therefore, BD must equal [tex]300\sqrt{3}\text{ ft}[/tex].
To find CD, we can subtract BC from BD. Notice that [tex]\triangle ABC[/tex] is also a 30-60-90 triangle. Therefore, since BC is the side opposite to the 30 degree angle, BC must equal [tex]\frac{300}{\sqrt{3}}=\frac{300\sqrt{3}}{3}}\text{ ft}[/tex]
Thus, the length of CD is equal to:
[tex]CD=BD-BC,\\CD=300\sqrt{3}-\frac{300\sqrt{3}}{3}=346.410161514\approx \boxed{346.4\text{ ft}}[/tex]
