Question

Destiny found that a maypole that is 12 meters tall casts a shadow 9 meters long. Then Destiny noticed a nearby radio tower that is 16 meters tall. How long is the radio tower's shadow?

Answer 1

To find the length of the radio tower's shadow, we use the ratio of the maypole's height to its shadow and set it equal to the ratio of the radio tower's height to its shadow. Solving the proportion, we find that the radio tower's shadow is 12 meters long.

Step-by-step explanation:

The length of the shadow cast by the radio tower can be determined by using the concept of similar triangles. The maypole and its shadow, as well as the radio tower and its shadow, form two sets of similar right-angled triangles. Therefore, their corresponding sides are in proportion. The height of the maypole is 12 meters, and it casts a 9-meter-long shadow. If the radio tower's height is 16 meters, we need to find the unknown length of its shadow, let's call it x.

• The proportions can be set up as follows: 12 meters / 9 meters = 16 meters / x
• Cross-multiplying gives us 12 * x = 16 * 9
• Dividing both sides by 12 gives us x = (16 * 9) / 12
• Calculating the right side, we find that x = 144 / 12 = 12 meters

Therefore, the radio tower's shadow is 12 meters long.