A tree $6\text{m}$ tall casts a $4\text{m}$ long shadow. At the same time, a flag pole casts a $50\text{m}$ long shadow. How long is the flag pole?

At any given instant, the angle of elevation of the sun is identical for nearby objects. Therefore, the ratio of the height of an object to the length of its shadow remains constant:
$$\frac{\text{Height of Tree}}{\text{Shadow of Tree}}=\frac{\text{Height of Flag Pole}}{\text{Shadow of Flag Pole}}$$

Let the height of the flag pole be $H$.

$$\frac{6}{4}=\frac{H}{50}$$

$$H=\frac{6\times 50}{4}$$

$$H=\frac{300}{4}=75\text{m}$$