Question

A park has a 3 meter tall tether ball pole and a 6.8 meter tall flagpole. The lengths of their shadows are proportional to their heights. What is the height of the tether ball pole if its shadow is 5 meters long?

Answer 1

The height of the tether ball pole is 2.14 meters.

Step-by-step explanation:

The relationship between the heights and shadows of objects in similar triangles is expressed by the formula:
`\( (height_1)/(shadow_1) = (height_2)/(shadow_2) \).` In this scenario, we can set up the proportion:
`\( (3)/(x) = (6.8)/(5) \)`, where 3 is the height of the tether ball pole, x is the length of its shadow, 6.8 is the height of the flagpole, and 5 is the length of its shadow. Solving for
`\( x \)`, we find that
`\( x = (3 * 5)/(6.8) \), which simplifies to \( x = 2.14 \).` Therefore, the height of the tether ball pole is 2.14 meters.

Understanding this involves recognizing the similarity of the triangles formed by the objects and their shadows. The proportionality of corresponding sides in similar triangles allows us to set up and solve the equation to find the unknown height. In this case, the height of the tether ball pole is determined by comparing the ratio of its height to the length of its shadow with the corresponding ratio of the flagpole. The final calculation confirms that the height of the tether ball pole is indeed 2.14 meters, showcasing the application of geometric principles to solve real-world problems.