Don't you just love related rates?

In summary, related rates are a mathematical concept used to calculate the rate of change of one variable with respect to another. They are useful for solving real-world problems involving changing quantities and can be applied to situations like a sliding ladder or a balloon's changing volume. Common techniques for solving related rates include creating a diagram, identifying variables, writing an equation, and using the chain rule. To improve understanding, practice and familiarize yourself with concepts and formulas, and seek out additional resources.
  • #1
ms. confused
91
0
The angle of elevation of the Sun is decreasing at a rate of 0.25 rad/h. How fast is the shadow cast by a 400-ft-tall building increasing when the angle of elevation of the Sun is π/6?

I thought about using the special triangle to find exact values for trig functions at π/6 but I don't know which equation I should use to relate the rate of change. What should I do? :uhh:
 
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  • #2
Just write [itex]L = H \cot \theta[/itex] with the obvious definitions and differentiate.
 

1. What are related rates?

Related rates are a mathematical concept that involves calculating the rate of change of one variable with respect to another variable. This can be applied to various real-world situations, such as the changing volume of a balloon or the rate at which a car is approaching a stop sign.

2. How are related rates useful?

Related rates can be useful in solving real-world problems that involve changing quantities. They allow us to understand the relationship between different variables and how they change over time.

3. Can you give an example of related rates in action?

One example of related rates is the classic ladder problem, where a ladder is leaning against a wall and sliding down. The rate at which the bottom of the ladder is moving can be related to the rate at which the top of the ladder is sliding down the wall.

4. What are some common techniques for solving related rates problems?

Some common techniques for solving related rates problems include creating a diagram, identifying and labeling the variables, writing an equation that relates the changing variables, and using the chain rule to differentiate the equation with respect to time.

5. How can I improve my understanding of related rates?

To improve your understanding of related rates, it is important to practice solving various types of problems and to familiarize yourself with the underlying concepts and formulas. You can also seek out additional resources, such as textbooks or online tutorials, to supplement your learning.

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