Trig derivative applications answer check

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SUMMARY

The discussion centers on calculating the rate of change of the base angle of an isosceles triangle with a fixed base of 20 cm and an altitude increasing at 1 cm/min when the area reaches 100 cm². The solution involves applying trigonometric derivatives and the area formula for triangles. A key point noted is the exact value of tan-1(1), which equals π/4, emphasizing the importance of precision in mathematical calculations.

PREREQUISITES
  • Understanding of trigonometric functions and their derivatives
  • Familiarity with the area formula for triangles
  • Knowledge of implicit differentiation techniques
  • Basic calculus concepts, including rates of change
NEXT STEPS
  • Study the application of implicit differentiation in related rates problems
  • Explore the derivation of the area formula for triangles
  • Learn about the properties of inverse trigonometric functions
  • Practice solving problems involving rates of change in geometric contexts
USEFUL FOR

Students studying calculus, particularly those focusing on related rates and trigonometric applications, as well as educators looking for examples of geometric rate problems.

spoc21
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Homework Statement



The base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At what rate is the base angle increasing when the area is 100 cm^2?

Homework Equations


The Attempt at a Solution



Im very unsure about my solution method. I have attached a copy my solution in pdf format, and would really appreciate if someone could take a quick look at it, and preferably tell me if its right or wrong..Thanks :smile:
 

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spoc21 said:

Homework Statement



The base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At what rate is the base angle increasing when the area is 100 cm^2?


Homework Equations





The Attempt at a Solution



Im very unsure about my solution method. I have attached a copy my solution in pdf format, and would really appreciate if someone could take a quick look at it, and preferably tell me if its right or wrong..


Thanks :smile:
Looks good with one very minor exception tan-1(1) = pi/4 (exactly), and is only approximately equal to .7854.
 

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