A flag pole on the top of a mall building is 75 m high. The height of the mall building is 325 m. To an observer at a height of 400 m, the mall building and the pole subtend equal angle $$\theta$$. If the horizontal distance of the observer from the pole is 'x', then what is the value of x?

In the given diagram AE is the mall building and DE is pole. The observer is at C point which is 400 mts from the ground. 

It is given that $$\angle$$DCE = $$\angle$$ECA = $$\theta$$

In $$\triangle$$ACD and $$\triangle$$ECD

tan(2$$\theta$$) = $$\frac{400}{x}$$

tan($$\theta$$) = $$\frac{75}{x}$$

We know that tan(2$$\theta$$) = $$\frac{2tan(\theta)}{1-tan^{2}(\theta)}$$

                  $$\therefore$$ $$\frac{400}{x}$$ = $$\frac{2*\frac{75}{x}}{1-(\frac{75}{x})^{2}}$$

                          $$x^{2}$$ = 9000 = $$30\sqrt{10}$$