Simple word problem: Chain rule

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Homework Help Overview

The problem involves a triangle where one side is increasing and another side is decreasing, while the area remains constant. The objective is to determine the rate of change of the angle between the sides given specific lengths and an initial angle.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks the formula for the angle between the two sides of the triangle, indicating uncertainty about how to express it in terms of the side lengths. Some participants suggest using trigonometric functions, while others propose geometric methods involving right triangles and area calculations.

Discussion Status

Participants are exploring different approaches to relate the sides of the triangle to the angle. Some guidance has been offered regarding the use of trigonometric functions and geometric constructions, but there is no explicit consensus on the method to be used.

Contextual Notes

The original poster expresses a lack of confidence in their trigonometry skills, which may affect their ability to engage with the suggested methods. There is also an implicit assumption that the area of the triangle is constant throughout the problem.

michonamona
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Homework Statement



One side of a triangle is increasing at a rate of 3cm/s and a second side is decreasing at a rate of 2cm/s. If the area of the triangle remain constant, at what rate does the angle between the sides change when the first side is 20cm long and the second side is 30cm, and the angle is pi/6?

Homework Equations





The Attempt at a Solution



My only question is, what is the formula for the angle between the two side? I know that it will be a function of the length of the two side, but I don't know how to find the explicit expression.

Thanks,
M
 
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Sines and cosines will serve you well.
 
Thanks, would you be so kind as to elaborate on your answer? I would appreciate it. My background in trigonometry is weak; although I do know how to use them on a right triangle, but in this case, I'm not quite certain.
 
Drop a perpendicular from one side to the other. That gives you a right triangle doesn't it? In that case you said you can do it. Then use area=(1/2)*base*height. If the two sides are a and b and the included angle is theta, what does that give you?
 
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