Firefighter Practice Exam

If a firefighter casts a shadow that is 7.5 feet long when the fire station casts a shadow of 35 feet, how tall is the fire station?

1. 27.5 feet

2. 28 feet

3. 29.7 feet

4. 32 feet

The correct answer is: 28 feet

To determine the height of the fire station using the lengths of the shadows, one can apply the principle of similar triangles. When two objects cast shadows, the height of the objects and the length of the shadows are proportionate to each other. In this scenario, the firefighter's shadow is 7.5 feet long, while the fire station's shadow is 35 feet long. The relationship can be expressed as a ratio, where the height of the firefighter (h) to the firefighter's shadow (7.5 feet) is equal to the height of the fire station (H) to the fire station's shadow (35 feet). This can be set up in the following proportion: h / 7.5 = H / 35 To find H, rearranging the equation allows for straightforward calculations: H = (35 * h) / 7.5 When using a standard firefighter height for this calculation, for example, the height of a firefighter could be assumed at about 6 feet: H = (35 * 6) / 7.5 H = 210 / 7.5 H = 28 feet This result indicates that when you use the proportion correctly, the calculated height of the fire station