Pregunta
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Noah is admiring a statue in Ashland Park from 6 meters away. If the distance between the top of the statue to Noah's head is 8 meters, how much taller is the statue than Noah? If necessary, round to the nearest tenth.

Ask by Mullins Savage. in the United States
Feb 24,2025

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The statue is approximately 5.3 meters taller than Noah.

Solución

Imagine a right triangle formed by: • The horizontal distance from Noah to the statue (6 m), • The vertical difference between the top of the statue and Noah’s head (which we need to find), and • The line-of-sight distance from Noah's head to the top of the statue (8 m). Using the Pythagorean theorem:  (horizontal side)² + (vertical side)² = (hypotenuse)² Let the vertical difference be x:  6² + x² = 8²  36 + x² = 64 Subtract 36 from both sides:  x² = 64 – 36 = 28 Now, take the square root:  x = √28 = 2√7 ≈ 5.3 meters Thus, the statue is approximately 5.3 meters taller than Noah.

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Extra Insights

To find how much taller the statue is than Noah, you can simply subtract the distance from Noah to the statue from the distance from the statue to Noah's head. So, you would take 8 meters (the distance from the statue's top to Noah's head) and subtract 6 meters (the distance Noah is standing from the statue). This gives you: 8 meters - 6 meters = 2 meters. Thus, the statue is 2 meters taller than Noah. Now you know that Noah is standing 6 meters away from the statue and the distance to the top of the statue is 8 meters. It’s important to always visualize such scenarios, as it can help you understand the relationships between different points in space. You might also want to explore similar problems involving angles and distances, as they can involve fascinating geometry and trigonometry concepts!

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