How to find value of x?

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Find the value of x.



Trail: Let consider the point between B and C is D. So $angle ADB =120^circ$ and $angle DAB =15^circ$. I believe that $angle DAC =30^circ$. But I am not sure. Please help me. Thanks in advance.




geometry trigonometry triangle




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    Why do you believe that $angle DAC = 30^circ$?
    – Babelfish
    Jul 25 at 7:48














up vote
0
down vote

favorite












enter image description here



Find the value of x.



Trail: Let consider the point between B and C is D. So $angle ADB =120^circ$ and $angle DAB =15^circ$. I believe that $angle DAC =30^circ$. But I am not sure. Please help me. Thanks in advance.




geometry trigonometry triangle




share|cite|improve this question

















  • 1




    Why do you believe that $angle DAC = 30^circ$?
    – Babelfish
    Jul 25 at 7:48












up vote
0
down vote

favorite









up vote
0
down vote

favorite











enter image description here



Find the value of x.



Trail: Let consider the point between B and C is D. So $angle ADB =120^circ$ and $angle DAB =15^circ$. I believe that $angle DAC =30^circ$. But I am not sure. Please help me. Thanks in advance.




geometry trigonometry triangle




share|cite|improve this question













enter image description here



Find the value of x.



Trail: Let consider the point between B and C is D. So $angle ADB =120^circ$ and $angle DAB =15^circ$. I believe that $angle DAC =30^circ$. But I am not sure. Please help me. Thanks in advance.





geometry trigonometry triangle





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 25 at 7:51









Babelfish

408112




408112









asked Jul 25 at 7:25









R DE

415




415







  • 1




    Why do you believe that $angle DAC = 30^circ$?
    – Babelfish
    Jul 25 at 7:48












  • 1




    Why do you believe that $angle DAC = 30^circ$?
    – Babelfish
    Jul 25 at 7:48







1




1




Why do you believe that $angle DAC = 30^circ$?
– Babelfish
Jul 25 at 7:48




Why do you believe that $angle DAC = 30^circ$?
– Babelfish
Jul 25 at 7:48










2 Answers
2






active

oldest

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up vote
0
down vote













Apply the Sine Rule to $Delta ADB$ and $Delta ABC$ to find two expressions for $AB$. That lets you relate $sin x$ to $sin(x+45)$. Then solve for $tan x$.






share|cite|improve this answer





















  • I try to solve it but I'm stuck. please help see my answer
    – R DE
    Jul 25 at 9:49

















up vote
0
down vote













So from $triangle ADB$ using sine rule, we get
$$fracsin 15 1=fracsin 120 AB=fracsin 45 AD$$
Similarly from $triangle ABC$ using sine rule, we get
$$fracsin (135-x) 3=fracsin x AB=fracsin 45 AC$$



So equating $AB$ from this two equations we get
$$fracsin (135-x) sin x =frac3sin 15 sin 120$$



Then I'm stuck.






share|cite|improve this answer

















  • 1




    Do you know $sin(x-y)=sin xcos y-cos xsin y$?
    – Empy2
    Jul 25 at 9:59










  • @Empy2 yes. how can I handle $#sin 15$?
    – R DE
    Jul 25 at 10:09






  • 1




    $sin15=sin(45-30)$
    – Empy2
    Jul 25 at 10:31










  • @RDE Were you able to finish the problem with Empy2's hint?
    – Robert Howard
    2 days ago










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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote













Apply the Sine Rule to $Delta ADB$ and $Delta ABC$ to find two expressions for $AB$. That lets you relate $sin x$ to $sin(x+45)$. Then solve for $tan x$.






share|cite|improve this answer





















  • I try to solve it but I'm stuck. please help see my answer
    – R DE
    Jul 25 at 9:49














up vote
0
down vote













Apply the Sine Rule to $Delta ADB$ and $Delta ABC$ to find two expressions for $AB$. That lets you relate $sin x$ to $sin(x+45)$. Then solve for $tan x$.






share|cite|improve this answer





















  • I try to solve it but I'm stuck. please help see my answer
    – R DE
    Jul 25 at 9:49












up vote
0
down vote










up vote
0
down vote









Apply the Sine Rule to $Delta ADB$ and $Delta ABC$ to find two expressions for $AB$. That lets you relate $sin x$ to $sin(x+45)$. Then solve for $tan x$.






share|cite|improve this answer













Apply the Sine Rule to $Delta ADB$ and $Delta ABC$ to find two expressions for $AB$. That lets you relate $sin x$ to $sin(x+45)$. Then solve for $tan x$.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Jul 25 at 7:47









Empy2

31.8k12059




31.8k12059











  • I try to solve it but I'm stuck. please help see my answer
    – R DE
    Jul 25 at 9:49
















  • I try to solve it but I'm stuck. please help see my answer
    – R DE
    Jul 25 at 9:49















I try to solve it but I'm stuck. please help see my answer
– R DE
Jul 25 at 9:49




I try to solve it but I'm stuck. please help see my answer
– R DE
Jul 25 at 9:49










up vote
0
down vote













So from $triangle ADB$ using sine rule, we get
$$fracsin 15 1=fracsin 120 AB=fracsin 45 AD$$
Similarly from $triangle ABC$ using sine rule, we get
$$fracsin (135-x) 3=fracsin x AB=fracsin 45 AC$$



So equating $AB$ from this two equations we get
$$fracsin (135-x) sin x =frac3sin 15 sin 120$$



Then I'm stuck.






share|cite|improve this answer

















  • 1




    Do you know $sin(x-y)=sin xcos y-cos xsin y$?
    – Empy2
    Jul 25 at 9:59










  • @Empy2 yes. how can I handle $#sin 15$?
    – R DE
    Jul 25 at 10:09






  • 1




    $sin15=sin(45-30)$
    – Empy2
    Jul 25 at 10:31










  • @RDE Were you able to finish the problem with Empy2's hint?
    – Robert Howard
    2 days ago














up vote
0
down vote













So from $triangle ADB$ using sine rule, we get
$$fracsin 15 1=fracsin 120 AB=fracsin 45 AD$$
Similarly from $triangle ABC$ using sine rule, we get
$$fracsin (135-x) 3=fracsin x AB=fracsin 45 AC$$



So equating $AB$ from this two equations we get
$$fracsin (135-x) sin x =frac3sin 15 sin 120$$



Then I'm stuck.






share|cite|improve this answer

















  • 1




    Do you know $sin(x-y)=sin xcos y-cos xsin y$?
    – Empy2
    Jul 25 at 9:59










  • @Empy2 yes. how can I handle $#sin 15$?
    – R DE
    Jul 25 at 10:09






  • 1




    $sin15=sin(45-30)$
    – Empy2
    Jul 25 at 10:31










  • @RDE Were you able to finish the problem with Empy2's hint?
    – Robert Howard
    2 days ago












up vote
0
down vote










up vote
0
down vote









So from $triangle ADB$ using sine rule, we get
$$fracsin 15 1=fracsin 120 AB=fracsin 45 AD$$
Similarly from $triangle ABC$ using sine rule, we get
$$fracsin (135-x) 3=fracsin x AB=fracsin 45 AC$$



So equating $AB$ from this two equations we get
$$fracsin (135-x) sin x =frac3sin 15 sin 120$$



Then I'm stuck.






share|cite|improve this answer













So from $triangle ADB$ using sine rule, we get
$$fracsin 15 1=fracsin 120 AB=fracsin 45 AD$$
Similarly from $triangle ABC$ using sine rule, we get
$$fracsin (135-x) 3=fracsin x AB=fracsin 45 AC$$



So equating $AB$ from this two equations we get
$$fracsin (135-x) sin x =frac3sin 15 sin 120$$



Then I'm stuck.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Jul 25 at 9:48









R DE

415




415







  • 1




    Do you know $sin(x-y)=sin xcos y-cos xsin y$?
    – Empy2
    Jul 25 at 9:59










  • @Empy2 yes. how can I handle $#sin 15$?
    – R DE
    Jul 25 at 10:09






  • 1




    $sin15=sin(45-30)$
    – Empy2
    Jul 25 at 10:31










  • @RDE Were you able to finish the problem with Empy2's hint?
    – Robert Howard
    2 days ago












  • 1




    Do you know $sin(x-y)=sin xcos y-cos xsin y$?
    – Empy2
    Jul 25 at 9:59










  • @Empy2 yes. how can I handle $#sin 15$?
    – R DE
    Jul 25 at 10:09






  • 1




    $sin15=sin(45-30)$
    – Empy2
    Jul 25 at 10:31










  • @RDE Were you able to finish the problem with Empy2's hint?
    – Robert Howard
    2 days ago







1




1




Do you know $sin(x-y)=sin xcos y-cos xsin y$?
– Empy2
Jul 25 at 9:59




Do you know $sin(x-y)=sin xcos y-cos xsin y$?
– Empy2
Jul 25 at 9:59












@Empy2 yes. how can I handle $#sin 15$?
– R DE
Jul 25 at 10:09




@Empy2 yes. how can I handle $#sin 15$?
– R DE
Jul 25 at 10:09




1




1




$sin15=sin(45-30)$
– Empy2
Jul 25 at 10:31




$sin15=sin(45-30)$
– Empy2
Jul 25 at 10:31












@RDE Were you able to finish the problem with Empy2's hint?
– Robert Howard
2 days ago




@RDE Were you able to finish the problem with Empy2's hint?
– Robert Howard
2 days ago












 

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