A triangle has sides $3x+1$, $x+2$, $x+3$ and an angle with a known cosine; find $x$ and area











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I'm having trouble with Question 10. I have figured out $x$, which is $2$. I'm not sure how I can find the area of the triangle. Please look at the attachment above.






trigonometry







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    up vote
    2
    down vote

    favorite
    1












    enter image description here



    I'm having trouble with Question 10. I have figured out $x$, which is $2$. I'm not sure how I can find the area of the triangle. Please look at the attachment above.






    trigonometry







    share|cite|improve this question









    New contributor




    Joshuap88 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.






















      up vote
      2
      down vote

      favorite
      1









      up vote
      2
      down vote

      favorite
      1






      1





      enter image description here



      I'm having trouble with Question 10. I have figured out $x$, which is $2$. I'm not sure how I can find the area of the triangle. Please look at the attachment above.






      trigonometry







      share|cite|improve this question









      New contributor




      Joshuap88 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      enter image description here



      I'm having trouble with Question 10. I have figured out $x$, which is $2$. I'm not sure how I can find the area of the triangle. Please look at the attachment above.






      trigonometry




      trigonometry






      share|cite|improve this question









      New contributor




      Joshuap88 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question









      New contributor




      Joshuap88 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|cite|improve this question




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      edited 1 hour ago









      Blue

      47k870148




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      asked 6 hours ago









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          2 Answers
          2






          active

          oldest

          votes

















          up vote
          4
          down vote













          If you have $x$, then you have all three side lengths. Now just apply Heron's formula.






          share|cite|improve this answer





















          • Thank you! This is definitely helpful if I don't have a calculator!
            – Joshuap88
            6 hours ago










          • @Joshuap88 You would still need to find $x$ using a calculator.
            – Toby Mak
            6 hours ago










          • @TobyMak $x$ can by surely found easily by hands from the quadratic equation obtined by the law of cosine.
            – gimusi
            5 hours ago










          • @BenW With your method how would you use the law of cosine?
            – gimusi
            5 hours ago






          • 1




            Didn't you use the law of cosines to find $x$? Now you no longer need it. Whether you use Heron's formula or $A=frac{1}{2}absintheta$, you are done with LoC.
            – Ben W
            5 hours ago




















          up vote
          4
          down vote













          HINT



          By law of cosine we have



          $$c^2 = a^2 + b^2-2abcos theta$$



          then we can find the area by



          $$A=frac12 absin theta$$






          share|cite|improve this answer





















          • Yeah, that's probably easier than Heron.
            – Ben W
            6 hours ago










          • @BenW Yes indeed I think that the idea and the spirit for the homework is that. But Heron is always good invoke :)
            – gimusi
            6 hours ago










          • @gimusi It's interesting that we get two solutions: one with $x = -frac{12}{11}$ and one with $x=2$.
            – Toby Mak
            6 hours ago










          • @TobyMak I didn't check that. I'll take a look.
            – gimusi
            6 hours ago






          • 1




            @TobyMak Sorry, I didn't see that clearly but of course we need to esclude -12/11 therefore x=2 is the good one!
            – gimusi
            5 hours ago











          Your Answer





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          2 Answers
          2






          active

          oldest

          votes








          2 Answers
          2






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

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          up vote
          4
          down vote













          If you have $x$, then you have all three side lengths. Now just apply Heron's formula.






          share|cite|improve this answer





















          • Thank you! This is definitely helpful if I don't have a calculator!
            – Joshuap88
            6 hours ago










          • @Joshuap88 You would still need to find $x$ using a calculator.
            – Toby Mak
            6 hours ago










          • @TobyMak $x$ can by surely found easily by hands from the quadratic equation obtined by the law of cosine.
            – gimusi
            5 hours ago










          • @BenW With your method how would you use the law of cosine?
            – gimusi
            5 hours ago






          • 1




            Didn't you use the law of cosines to find $x$? Now you no longer need it. Whether you use Heron's formula or $A=frac{1}{2}absintheta$, you are done with LoC.
            – Ben W
            5 hours ago

















          up vote
          4
          down vote













          If you have $x$, then you have all three side lengths. Now just apply Heron's formula.






          share|cite|improve this answer





















          • Thank you! This is definitely helpful if I don't have a calculator!
            – Joshuap88
            6 hours ago










          • @Joshuap88 You would still need to find $x$ using a calculator.
            – Toby Mak
            6 hours ago










          • @TobyMak $x$ can by surely found easily by hands from the quadratic equation obtined by the law of cosine.
            – gimusi
            5 hours ago










          • @BenW With your method how would you use the law of cosine?
            – gimusi
            5 hours ago






          • 1




            Didn't you use the law of cosines to find $x$? Now you no longer need it. Whether you use Heron's formula or $A=frac{1}{2}absintheta$, you are done with LoC.
            – Ben W
            5 hours ago















          up vote
          4
          down vote










          up vote
          4
          down vote









          If you have $x$, then you have all three side lengths. Now just apply Heron's formula.






          share|cite|improve this answer












          If you have $x$, then you have all three side lengths. Now just apply Heron's formula.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 6 hours ago









          Ben W

          1,234510




          1,234510












          • Thank you! This is definitely helpful if I don't have a calculator!
            – Joshuap88
            6 hours ago










          • @Joshuap88 You would still need to find $x$ using a calculator.
            – Toby Mak
            6 hours ago










          • @TobyMak $x$ can by surely found easily by hands from the quadratic equation obtined by the law of cosine.
            – gimusi
            5 hours ago










          • @BenW With your method how would you use the law of cosine?
            – gimusi
            5 hours ago






          • 1




            Didn't you use the law of cosines to find $x$? Now you no longer need it. Whether you use Heron's formula or $A=frac{1}{2}absintheta$, you are done with LoC.
            – Ben W
            5 hours ago




















          • Thank you! This is definitely helpful if I don't have a calculator!
            – Joshuap88
            6 hours ago










          • @Joshuap88 You would still need to find $x$ using a calculator.
            – Toby Mak
            6 hours ago










          • @TobyMak $x$ can by surely found easily by hands from the quadratic equation obtined by the law of cosine.
            – gimusi
            5 hours ago










          • @BenW With your method how would you use the law of cosine?
            – gimusi
            5 hours ago






          • 1




            Didn't you use the law of cosines to find $x$? Now you no longer need it. Whether you use Heron's formula or $A=frac{1}{2}absintheta$, you are done with LoC.
            – Ben W
            5 hours ago


















          Thank you! This is definitely helpful if I don't have a calculator!
          – Joshuap88
          6 hours ago




          Thank you! This is definitely helpful if I don't have a calculator!
          – Joshuap88
          6 hours ago












          @Joshuap88 You would still need to find $x$ using a calculator.
          – Toby Mak
          6 hours ago




          @Joshuap88 You would still need to find $x$ using a calculator.
          – Toby Mak
          6 hours ago












          @TobyMak $x$ can by surely found easily by hands from the quadratic equation obtined by the law of cosine.
          – gimusi
          5 hours ago




          @TobyMak $x$ can by surely found easily by hands from the quadratic equation obtined by the law of cosine.
          – gimusi
          5 hours ago












          @BenW With your method how would you use the law of cosine?
          – gimusi
          5 hours ago




          @BenW With your method how would you use the law of cosine?
          – gimusi
          5 hours ago




          1




          1




          Didn't you use the law of cosines to find $x$? Now you no longer need it. Whether you use Heron's formula or $A=frac{1}{2}absintheta$, you are done with LoC.
          – Ben W
          5 hours ago






          Didn't you use the law of cosines to find $x$? Now you no longer need it. Whether you use Heron's formula or $A=frac{1}{2}absintheta$, you are done with LoC.
          – Ben W
          5 hours ago












          up vote
          4
          down vote













          HINT



          By law of cosine we have



          $$c^2 = a^2 + b^2-2abcos theta$$



          then we can find the area by



          $$A=frac12 absin theta$$






          share|cite|improve this answer





















          • Yeah, that's probably easier than Heron.
            – Ben W
            6 hours ago










          • @BenW Yes indeed I think that the idea and the spirit for the homework is that. But Heron is always good invoke :)
            – gimusi
            6 hours ago










          • @gimusi It's interesting that we get two solutions: one with $x = -frac{12}{11}$ and one with $x=2$.
            – Toby Mak
            6 hours ago










          • @TobyMak I didn't check that. I'll take a look.
            – gimusi
            6 hours ago






          • 1




            @TobyMak Sorry, I didn't see that clearly but of course we need to esclude -12/11 therefore x=2 is the good one!
            – gimusi
            5 hours ago















          up vote
          4
          down vote













          HINT



          By law of cosine we have



          $$c^2 = a^2 + b^2-2abcos theta$$



          then we can find the area by



          $$A=frac12 absin theta$$






          share|cite|improve this answer





















          • Yeah, that's probably easier than Heron.
            – Ben W
            6 hours ago










          • @BenW Yes indeed I think that the idea and the spirit for the homework is that. But Heron is always good invoke :)
            – gimusi
            6 hours ago










          • @gimusi It's interesting that we get two solutions: one with $x = -frac{12}{11}$ and one with $x=2$.
            – Toby Mak
            6 hours ago










          • @TobyMak I didn't check that. I'll take a look.
            – gimusi
            6 hours ago






          • 1




            @TobyMak Sorry, I didn't see that clearly but of course we need to esclude -12/11 therefore x=2 is the good one!
            – gimusi
            5 hours ago













          up vote
          4
          down vote










          up vote
          4
          down vote









          HINT



          By law of cosine we have



          $$c^2 = a^2 + b^2-2abcos theta$$



          then we can find the area by



          $$A=frac12 absin theta$$






          share|cite|improve this answer












          HINT



          By law of cosine we have



          $$c^2 = a^2 + b^2-2abcos theta$$



          then we can find the area by



          $$A=frac12 absin theta$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 6 hours ago









          gimusi

          89.4k74495




          89.4k74495












          • Yeah, that's probably easier than Heron.
            – Ben W
            6 hours ago










          • @BenW Yes indeed I think that the idea and the spirit for the homework is that. But Heron is always good invoke :)
            – gimusi
            6 hours ago










          • @gimusi It's interesting that we get two solutions: one with $x = -frac{12}{11}$ and one with $x=2$.
            – Toby Mak
            6 hours ago










          • @TobyMak I didn't check that. I'll take a look.
            – gimusi
            6 hours ago






          • 1




            @TobyMak Sorry, I didn't see that clearly but of course we need to esclude -12/11 therefore x=2 is the good one!
            – gimusi
            5 hours ago


















          • Yeah, that's probably easier than Heron.
            – Ben W
            6 hours ago










          • @BenW Yes indeed I think that the idea and the spirit for the homework is that. But Heron is always good invoke :)
            – gimusi
            6 hours ago










          • @gimusi It's interesting that we get two solutions: one with $x = -frac{12}{11}$ and one with $x=2$.
            – Toby Mak
            6 hours ago










          • @TobyMak I didn't check that. I'll take a look.
            – gimusi
            6 hours ago






          • 1




            @TobyMak Sorry, I didn't see that clearly but of course we need to esclude -12/11 therefore x=2 is the good one!
            – gimusi
            5 hours ago
















          Yeah, that's probably easier than Heron.
          – Ben W
          6 hours ago




          Yeah, that's probably easier than Heron.
          – Ben W
          6 hours ago












          @BenW Yes indeed I think that the idea and the spirit for the homework is that. But Heron is always good invoke :)
          – gimusi
          6 hours ago




          @BenW Yes indeed I think that the idea and the spirit for the homework is that. But Heron is always good invoke :)
          – gimusi
          6 hours ago












          @gimusi It's interesting that we get two solutions: one with $x = -frac{12}{11}$ and one with $x=2$.
          – Toby Mak
          6 hours ago




          @gimusi It's interesting that we get two solutions: one with $x = -frac{12}{11}$ and one with $x=2$.
          – Toby Mak
          6 hours ago












          @TobyMak I didn't check that. I'll take a look.
          – gimusi
          6 hours ago




          @TobyMak I didn't check that. I'll take a look.
          – gimusi
          6 hours ago




          1




          1




          @TobyMak Sorry, I didn't see that clearly but of course we need to esclude -12/11 therefore x=2 is the good one!
          – gimusi
          5 hours ago




          @TobyMak Sorry, I didn't see that clearly but of course we need to esclude -12/11 therefore x=2 is the good one!
          – gimusi
          5 hours ago










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