Final answer:
To solve this problem, set up a proportion between the heights and lengths of the shadows. The options that satisfy the proportion are 1.8 meters and 4.08 meters, or 0.6 meters and 1.36 meters.
Step-by-step explanation:
To solve this problem, we can set up a proportion between the heights and the lengths of the shadows. Let's call the height of the tether ball pole 'h1', the height of the flagpole 'h2', the length of the tether ball pole shadow 's1', and the length of the flagpole shadow 's2'. The proportion is: h1/h2 = s1/s2.
We can now plug in the values given in each option and see which one satisfies the proportion. Let's go through each option:
- Tether ball pole shadow: 1.35 meters, Flagpole shadow: 3.4 meters. h1/h2 = 3/6.8 = 0.441, s1/s2 = 1.35/3.4 = 0.397. These two ratios are not equal, so this option is not correct.
- Tether ball pole shadow: 1.8 meters, Flagpole shadow: 4.08 meters. h1/h2 = 3/6.8 = 0.441, s1/s2 = 1.8/4.08 = 0.441. These two ratios are equal, so this option could be correct.
- Tether ball pole shadow: 3.75 meters, Flagpole shadow: 8.35 meters. h1/h2 = 3/6.8 = 0.441, s1/s2 = 3.75/8.35 = 0.449. These two ratios are not equal, so this option is not correct.
- Tether ball pole shadow: 0.6 meters, Flagpole shadow: 1.36 meters. h1/h2 = 3/6.8 = 0.441, s1/s2 = 0.6/1.36 = 0.441. These two ratios are equal, so this option could be correct.
- Tether ball pole shadow: 2 meters, Flagpole shadow: 4.8 meters. h1/h2 = 3/6.8 = 0.441, s1/s2 = 2/4.8 = 0.417. These two ratios are not equal, so this option is not correct.
Based on these calculations, options 2 and 4 could be correct because the ratios of the heights are equal to the ratios of the shadow lengths. Therefore, the lengths of the shadows could be 1.8 meters and 4.08 meters, or 0.6 meters and 1.36 meters.