A tall pole is constructed in a flat parking lot; the pole stands straight up and forms a right angle with the ground. The pole casts a shadow, as shown below. The length of the shadow is $22$ feet. Find the height of the pole, to the nearest foot. You may use a calculator.
By similar triangles, we have the proportion $\frac{105}{h} = \frac{22}{h + 4}$, where $h$ is the height of the pole. Cross-multiplying gives $22h = 105h + 420$, so $83h = 420$. Hence, $h \approx \boxed{5.06}$ feet.
