Stuck on a Related Rates Triangle Problem

In summary, the conversation is about a person seeking help with a related rates question involving the height and area of an equilateral triangle. They are stuck on how to use the chain rule to solve the problem and are provided with some equations to consider.
  • #1
scorpa
367
1
Hi Again,

I am doing a question on related rates that I have become stuck on.

The height (h) of an equilateral triangle is increasing at a rate of 3cm/min. How fast is the area changing when h is 5cm?

I know that the area of a triangle is bh/2, but after that I am stuck :redface: I tried deriving it using the chain rule so that I could substitute h and the rate of h, but I don't think that i was doing it the right way. If anyone could direct me here I would really appreciate the help.
 
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  • #2
Here are some things to consider, the height "h" of an equilateral triangle is

[tex]\frac{1}{2}\sqrt{3}s[/tex]

where "s" is the length of one side.

The area of this triangle is equal to

[tex]\frac{1}{2}sh[/tex]

See any substitutions?
 
  • #3
[tex]
\frac{dA}{dt} = \frac{dh}{dt} * \frac{dA}{dh}
[/tex]
 

FAQ: Stuck on a Related Rates Triangle Problem

1. What is a related rates triangle problem?

A related rates triangle problem is a type of mathematical problem that involves finding the rate of change of one side of a triangle while the other sides are also changing. This type of problem typically involves the use of trigonometry and the chain rule.

2. How do you approach a related rates triangle problem?

The first step in approaching a related rates triangle problem is to clearly define the variables involved and draw a diagram of the triangle. Then, use the given information to set up an equation that relates the changing variables. Finally, use calculus techniques, such as the chain rule, to solve for the desired rate of change.

3. What are some common mistakes to avoid when solving a related rates triangle problem?

One common mistake when solving a related rates triangle problem is not properly identifying and labeling the changing variables. Another mistake is not setting up the equation correctly or not using the chain rule correctly. It is also important to carefully consider the units of measurement and make sure they are consistent throughout the problem.

4. Can you provide an example of a related rates triangle problem?

Sure, here is an example: A ladder is leaning against a wall and sliding down at a rate of 2 feet per second. If the bottom of the ladder is 10 feet away from the wall, how fast is the top of the ladder sliding down the wall when the bottom is 6 feet away from the wall? This problem involves finding the rate of change of the height of the triangle (ladder) while the distance from the wall is also changing.

5. How can related rates triangle problems be applied in real life?

Related rates triangle problems can be applied in various real-life scenarios, such as calculating the rate of change of the water level in a tank, the speed of an airplane as it travels on a curved path, or the growth rate of a tree leaning against a wall. These types of problems can also be found in engineering and physics to analyze the motion of objects.

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