Related Rates Integration

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A right angled triangle ABC has a fixed hypotenuse AC of length 10. Side AB increases at 0.1 cm/s. At what rate is the angle CAB increasing when the triangle is isosceles.



My try:

Let x = side AB. Therefore dx/dt= 0.1 cm/s

let angle CAB = y



cos(y)=x/10
therefore dy/dt=-1/100sin(y) (radians/second).



Now i need to find the angle y for when the triangle is isosceles i.e. x=10. I have tried many ways but i just cannot find angle y whatsoever. I don't know what to do. Am i missing something obvious?






calculus integration







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    up vote
    1
    down vote

    favorite












    A right angled triangle ABC has a fixed hypotenuse AC of length 10. Side AB increases at 0.1 cm/s. At what rate is the angle CAB increasing when the triangle is isosceles.



    My try:

    Let x = side AB. Therefore dx/dt= 0.1 cm/s

    let angle CAB = y



    cos(y)=x/10
    therefore dy/dt=-1/100sin(y) (radians/second).



    Now i need to find the angle y for when the triangle is isosceles i.e. x=10. I have tried many ways but i just cannot find angle y whatsoever. I don't know what to do. Am i missing something obvious?






    calculus integration







    share|cite|improve this question

























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      A right angled triangle ABC has a fixed hypotenuse AC of length 10. Side AB increases at 0.1 cm/s. At what rate is the angle CAB increasing when the triangle is isosceles.



      My try:

      Let x = side AB. Therefore dx/dt= 0.1 cm/s

      let angle CAB = y



      cos(y)=x/10
      therefore dy/dt=-1/100sin(y) (radians/second).



      Now i need to find the angle y for when the triangle is isosceles i.e. x=10. I have tried many ways but i just cannot find angle y whatsoever. I don't know what to do. Am i missing something obvious?






      calculus integration







      share|cite|improve this question















      A right angled triangle ABC has a fixed hypotenuse AC of length 10. Side AB increases at 0.1 cm/s. At what rate is the angle CAB increasing when the triangle is isosceles.



      My try:

      Let x = side AB. Therefore dx/dt= 0.1 cm/s

      let angle CAB = y



      cos(y)=x/10
      therefore dy/dt=-1/100sin(y) (radians/second).



      Now i need to find the angle y for when the triangle is isosceles i.e. x=10. I have tried many ways but i just cannot find angle y whatsoever. I don't know what to do. Am i missing something obvious?






      calculus integration




      calculus integration






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      edited Aug 31 at 2:31









      gt6989b

      30.7k22248




      30.7k22248










      asked Aug 31 at 2:23









      Deep Patel

      63




      63




















          1 Answer
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          HINT



          The triangle is isosceles when $AB = x = BC$ so by the Pythagorean Theorem you have
          $$
          x^2+x^2=10^2 iff x = sqrt50 = 5sqrt2.
          $$






          share|cite|improve this answer




















          • but when the triangle is iscosceles, you cant use the pythag theorem right. When the triangle is iscosceles, i know what x is, x=10. But i need to find the top angle (y) of this isosceles triangle.
            – Deep Patel
            Aug 31 at 2:43











          Your Answer




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          1 Answer
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          active

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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          0
          down vote













          HINT



          The triangle is isosceles when $AB = x = BC$ so by the Pythagorean Theorem you have
          $$
          x^2+x^2=10^2 iff x = sqrt50 = 5sqrt2.
          $$






          share|cite|improve this answer




















          • but when the triangle is iscosceles, you cant use the pythag theorem right. When the triangle is iscosceles, i know what x is, x=10. But i need to find the top angle (y) of this isosceles triangle.
            – Deep Patel
            Aug 31 at 2:43















          up vote
          0
          down vote













          HINT



          The triangle is isosceles when $AB = x = BC$ so by the Pythagorean Theorem you have
          $$
          x^2+x^2=10^2 iff x = sqrt50 = 5sqrt2.
          $$






          share|cite|improve this answer




















          • but when the triangle is iscosceles, you cant use the pythag theorem right. When the triangle is iscosceles, i know what x is, x=10. But i need to find the top angle (y) of this isosceles triangle.
            – Deep Patel
            Aug 31 at 2:43













          up vote
          0
          down vote










          up vote
          0
          down vote









          HINT



          The triangle is isosceles when $AB = x = BC$ so by the Pythagorean Theorem you have
          $$
          x^2+x^2=10^2 iff x = sqrt50 = 5sqrt2.
          $$






          share|cite|improve this answer












          HINT



          The triangle is isosceles when $AB = x = BC$ so by the Pythagorean Theorem you have
          $$
          x^2+x^2=10^2 iff x = sqrt50 = 5sqrt2.
          $$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 31 at 2:36









          gt6989b

          30.7k22248




          30.7k22248











          • but when the triangle is iscosceles, you cant use the pythag theorem right. When the triangle is iscosceles, i know what x is, x=10. But i need to find the top angle (y) of this isosceles triangle.
            – Deep Patel
            Aug 31 at 2:43

















          • but when the triangle is iscosceles, you cant use the pythag theorem right. When the triangle is iscosceles, i know what x is, x=10. But i need to find the top angle (y) of this isosceles triangle.
            – Deep Patel
            Aug 31 at 2:43
















          but when the triangle is iscosceles, you cant use the pythag theorem right. When the triangle is iscosceles, i know what x is, x=10. But i need to find the top angle (y) of this isosceles triangle.
          – Deep Patel
          Aug 31 at 2:43





          but when the triangle is iscosceles, you cant use the pythag theorem right. When the triangle is iscosceles, i know what x is, x=10. But i need to find the top angle (y) of this isosceles triangle.
          – Deep Patel
          Aug 31 at 2:43


















           

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