Is it mathematically right to convert triangle it to such a circle like that?
up vote
1
down vote
favorite
Given that
$$hat{ABC} = 26^circ, hat{ACB} = 52^circ, |AC| = 11, [AB] perp [AD] $$
Evaluate $|BD| = x $.
I want to change my point of view against these type of questions. What if we consider that this is a circle? Below I drew a diagram
Is it mathematically right to convert triangle it to such a circle like that? If yes, how can we take it from there?
Regards
geometry triangle circle
asked Nov 27 at 20:47
Enzo
996
|
show 6 more comments
up vote
1
down vote
favorite
Given that
$$hat{ABC} = 26^circ, hat{ACB} = 52^circ, |AC| = 11, [AB] perp [AD] $$
Evaluate $|BD| = x $.
I want to change my point of view against these type of questions. What if we consider that this is a circle? Below I drew a diagram
Is it mathematically right to convert triangle it to such a circle like that? If yes, how can we take it from there?
Regards
geometry triangle circle
asked Nov 27 at 20:47
Enzo
996
1
You can draw a circle around triangle any time, but it does not necesery lead you to the solution.
– greedoid
Nov 27 at 20:49
2
I would use the word "inscribe" and not "convert" (i.e. inscribe the triangle in the circle). While there isn't anything wrong with it, does it really help you get to a solution? My guess would be no, but always open to new ideas.
– Aditya Dua
Nov 27 at 20:52
Hints: What are the internal angles of a triangle? What's the sum of angles in a straight line?
– Jam
Nov 27 at 20:56
Oh so, instead of directly solving the question, I need your dear assistance to change my perspective because I'm really having issues whenever I attempt to solve a question in triangles. For instance, doing what would make the question clear? I also found all angles.
– Enzo
Nov 27 at 20:59
2
@Jam Sure thing! I know Sine's theorem which states that $dfrac{a}{sin A} = dfrac{b}{sin A} = dfrac{c}{sin C}$. However, I'm also looking for strategy/method that makes it more clear than it is in this situtation.
– Enzo
Nov 27 at 21:04
|
show 6 more comments
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Given that
$$hat{ABC} = 26^circ, hat{ACB} = 52^circ, |AC| = 11, [AB] perp [AD] $$
Evaluate $|BD| = x $.
I want to change my point of view against these type of questions. What if we consider that this is a circle? Below I drew a diagram
Is it mathematically right to convert triangle it to such a circle like that? If yes, how can we take it from there?
Regards
geometry triangle circle
asked Nov 27 at 20:47
Enzo
996
Given that
$$hat{ABC} = 26^circ, hat{ACB} = 52^circ, |AC| = 11, [AB] perp [AD] $$
Evaluate $|BD| = x $.
I want to change my point of view against these type of questions. What if we consider that this is a circle? Below I drew a diagram
Is it mathematically right to convert triangle it to such a circle like that? If yes, how can we take it from there?
Regards
geometry triangle circle
geometry triangle circle
asked Nov 27 at 20:47
Enzo
996
asked Nov 27 at 20:47
Enzo
996
asked Nov 27 at 20:47
Enzo
996
asked Nov 27 at 20:47
Enzo
996
asked Nov 27 at 20:47
Enzo
996
996
1
You can draw a circle around triangle any time, but it does not necesery lead you to the solution.
– greedoid
Nov 27 at 20:49
2
I would use the word "inscribe" and not "convert" (i.e. inscribe the triangle in the circle). While there isn't anything wrong with it, does it really help you get to a solution? My guess would be no, but always open to new ideas.
– Aditya Dua
Nov 27 at 20:52
Hints: What are the internal angles of a triangle? What's the sum of angles in a straight line?
– Jam
Nov 27 at 20:56
Oh so, instead of directly solving the question, I need your dear assistance to change my perspective because I'm really having issues whenever I attempt to solve a question in triangles. For instance, doing what would make the question clear? I also found all angles.
– Enzo
Nov 27 at 20:59
2
@Jam Sure thing! I know Sine's theorem which states that $dfrac{a}{sin A} = dfrac{b}{sin A} = dfrac{c}{sin C}$. However, I'm also looking for strategy/method that makes it more clear than it is in this situtation.
– Enzo
Nov 27 at 21:04
|
show 6 more comments
1
You can draw a circle around triangle any time, but it does not necesery lead you to the solution.
– greedoid
Nov 27 at 20:49
2
I would use the word "inscribe" and not "convert" (i.e. inscribe the triangle in the circle). While there isn't anything wrong with it, does it really help you get to a solution? My guess would be no, but always open to new ideas.
– Aditya Dua
Nov 27 at 20:52
Hints: What are the internal angles of a triangle? What's the sum of angles in a straight line?
– Jam
Nov 27 at 20:56
Oh so, instead of directly solving the question, I need your dear assistance to change my perspective because I'm really having issues whenever I attempt to solve a question in triangles. For instance, doing what would make the question clear? I also found all angles.
– Enzo
Nov 27 at 20:59
2
@Jam Sure thing! I know Sine's theorem which states that $dfrac{a}{sin A} = dfrac{b}{sin A} = dfrac{c}{sin C}$. However, I'm also looking for strategy/method that makes it more clear than it is in this situtation.
– Enzo
Nov 27 at 21:04
1
1
You can draw a circle around triangle any time, but it does not necesery lead you to the solution.
– greedoid
Nov 27 at 20:49
You can draw a circle around triangle any time, but it does not necesery lead you to the solution.
– greedoid
Nov 27 at 20:49
2
2
I would use the word "inscribe" and not "convert" (i.e. inscribe the triangle in the circle). While there isn't anything wrong with it, does it really help you get to a solution? My guess would be no, but always open to new ideas.
– Aditya Dua
Nov 27 at 20:52
I would use the word "inscribe" and not "convert" (i.e. inscribe the triangle in the circle). While there isn't anything wrong with it, does it really help you get to a solution? My guess would be no, but always open to new ideas.
– Aditya Dua
Nov 27 at 20:52
Hints: What are the internal angles of a triangle? What's the sum of angles in a straight line?
– Jam
Nov 27 at 20:56
Hints: What are the internal angles of a triangle? What's the sum of angles in a straight line?
– Jam
Nov 27 at 20:56
Oh so, instead of directly solving the question, I need your dear assistance to change my perspective because I'm really having issues whenever I attempt to solve a question in triangles. For instance, doing what would make the question clear? I also found all angles.
– Enzo
Nov 27 at 20:59
Oh so, instead of directly solving the question, I need your dear assistance to change my perspective because I'm really having issues whenever I attempt to solve a question in triangles. For instance, doing what would make the question clear? I also found all angles.
– Enzo
Nov 27 at 20:59
2
2
@Jam Sure thing! I know Sine's theorem which states that $dfrac{a}{sin A} = dfrac{b}{sin A} = dfrac{c}{sin C}$. However, I'm also looking for strategy/method that makes it more clear than it is in this situtation.
– Enzo
Nov 27 at 21:04
@Jam Sure thing! I know Sine's theorem which states that $dfrac{a}{sin A} = dfrac{b}{sin A} = dfrac{c}{sin C}$. However, I'm also looking for strategy/method that makes it more clear than it is in this situtation.
– Enzo
Nov 27 at 21:04
|
show 6 more comments
2 Answers
2
active
oldest
votes
up vote
1
down vote
If we want to use the sine law, to get $x$ we need to look at triangle $BAD$. $$frac x{sin 90^circ}=frac{AD}{sin 26^circ}$$
We don't know $AD$, but we can once again apply the sine law in the $DAC$ triangle. $$frac{AD}{sin 52^circ}=frac{AC}{sin angle{ADC}}$$
You know $AC=11$ and you can get the angle $angle ADC$ since it's a supplement of $angle ADB$, and you know all angles in that triangle.
edited Nov 27 at 22:39
math818
33
answered Nov 27 at 21:48
Andrei
10.8k21025
From $frac{AD}{sin 52^circ}=dfrac{AC}{sin angle{ADC}}$, do we get that $dfrac{AD}{sin 52^circ}=dfrac{11}{sin 116^circ}$?
– Enzo
Nov 27 at 21:51
No. What's the $ADC$ angle? If you know it, you can get $AD$.
– Andrei
Nov 27 at 21:54
Isn't it $hat{ADC} = 116$?
– Enzo
Nov 27 at 21:58
Correct. Now find $AD$ from my second equation. Then use it in the first equation, to find $x$.
– Andrei
Nov 27 at 21:59
add a comment |
up vote
0
down vote
Knowing $angle ABD$ and $angle BAD$ you can solve for $angle ADB$ $$angle ADB=180°-26°-90°=64°$$ The angles $angle ADB$ and $angle ADC$ are supplementary, so $angle ADC=116°$. Knowing angles $angle ADC, angle ACD$, and the length of $AC$, the law of sines can be used to solve for the length of $AD$.
$$frac{11}{sin(116)}=frac{AD}{sin(52)}Rightarrow AD=frac{11sin(52)}{sin(116)}approx9,64$$ The law of sines can be used again to find $x$. $$frac{9.64}{sin(26)}=frac{x}{sin(90)}rightarrow x=frac{9.64sin(90)}{sin(26)}$$ $x$ is 22.
That is how I would do it. Sorry about the format, I am not familiar with the equation makers.
edited Nov 27 at 23:35
Dr. Mathva
926315
answered Nov 27 at 22:34
math818
33
add a comment |
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2 Answers
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2 Answers
2
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active
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up vote
1
down vote
If we want to use the sine law, to get $x$ we need to look at triangle $BAD$. $$frac x{sin 90^circ}=frac{AD}{sin 26^circ}$$
We don't know $AD$, but we can once again apply the sine law in the $DAC$ triangle. $$frac{AD}{sin 52^circ}=frac{AC}{sin angle{ADC}}$$
You know $AC=11$ and you can get the angle $angle ADC$ since it's a supplement of $angle ADB$, and you know all angles in that triangle.
edited Nov 27 at 22:39
math818
33
answered Nov 27 at 21:48
Andrei
10.8k21025
From $frac{AD}{sin 52^circ}=dfrac{AC}{sin angle{ADC}}$, do we get that $dfrac{AD}{sin 52^circ}=dfrac{11}{sin 116^circ}$?
– Enzo
Nov 27 at 21:51
No. What's the $ADC$ angle? If you know it, you can get $AD$.
– Andrei
Nov 27 at 21:54
Isn't it $hat{ADC} = 116$?
– Enzo
Nov 27 at 21:58
Correct. Now find $AD$ from my second equation. Then use it in the first equation, to find $x$.
– Andrei
Nov 27 at 21:59
add a comment |
up vote
1
down vote
If we want to use the sine law, to get $x$ we need to look at triangle $BAD$. $$frac x{sin 90^circ}=frac{AD}{sin 26^circ}$$
We don't know $AD$, but we can once again apply the sine law in the $DAC$ triangle. $$frac{AD}{sin 52^circ}=frac{AC}{sin angle{ADC}}$$
You know $AC=11$ and you can get the angle $angle ADC$ since it's a supplement of $angle ADB$, and you know all angles in that triangle.
edited Nov 27 at 22:39
math818
33
answered Nov 27 at 21:48
Andrei
10.8k21025
From $frac{AD}{sin 52^circ}=dfrac{AC}{sin angle{ADC}}$, do we get that $dfrac{AD}{sin 52^circ}=dfrac{11}{sin 116^circ}$?
– Enzo
Nov 27 at 21:51
No. What's the $ADC$ angle? If you know it, you can get $AD$.
– Andrei
Nov 27 at 21:54
Isn't it $hat{ADC} = 116$?
– Enzo
Nov 27 at 21:58
Correct. Now find $AD$ from my second equation. Then use it in the first equation, to find $x$.
– Andrei
Nov 27 at 21:59
add a comment |
up vote
1
down vote
up vote
1
down vote
If we want to use the sine law, to get $x$ we need to look at triangle $BAD$. $$frac x{sin 90^circ}=frac{AD}{sin 26^circ}$$
We don't know $AD$, but we can once again apply the sine law in the $DAC$ triangle. $$frac{AD}{sin 52^circ}=frac{AC}{sin angle{ADC}}$$
You know $AC=11$ and you can get the angle $angle ADC$ since it's a supplement of $angle ADB$, and you know all angles in that triangle.
edited Nov 27 at 22:39
math818
33
answered Nov 27 at 21:48
Andrei
10.8k21025
If we want to use the sine law, to get $x$ we need to look at triangle $BAD$. $$frac x{sin 90^circ}=frac{AD}{sin 26^circ}$$
We don't know $AD$, but we can once again apply the sine law in the $DAC$ triangle. $$frac{AD}{sin 52^circ}=frac{AC}{sin angle{ADC}}$$
You know $AC=11$ and you can get the angle $angle ADC$ since it's a supplement of $angle ADB$, and you know all angles in that triangle.
edited Nov 27 at 22:39
math818
33
answered Nov 27 at 21:48
Andrei
10.8k21025
edited Nov 27 at 22:39
math818
33
edited Nov 27 at 22:39
math818
33
edited Nov 27 at 22:39
math818
33
33
answered Nov 27 at 21:48
Andrei
10.8k21025
answered Nov 27 at 21:48
Andrei
10.8k21025
answered Nov 27 at 21:48
Andrei
10.8k21025
10.8k21025
From $frac{AD}{sin 52^circ}=dfrac{AC}{sin angle{ADC}}$, do we get that $dfrac{AD}{sin 52^circ}=dfrac{11}{sin 116^circ}$?
– Enzo
Nov 27 at 21:51
No. What's the $ADC$ angle? If you know it, you can get $AD$.
– Andrei
Nov 27 at 21:54
Isn't it $hat{ADC} = 116$?
– Enzo
Nov 27 at 21:58
Correct. Now find $AD$ from my second equation. Then use it in the first equation, to find $x$.
– Andrei
Nov 27 at 21:59
add a comment |
From $frac{AD}{sin 52^circ}=dfrac{AC}{sin angle{ADC}}$, do we get that $dfrac{AD}{sin 52^circ}=dfrac{11}{sin 116^circ}$?
– Enzo
Nov 27 at 21:51
No. What's the $ADC$ angle? If you know it, you can get $AD$.
– Andrei
Nov 27 at 21:54
Isn't it $hat{ADC} = 116$?
– Enzo
Nov 27 at 21:58
Correct. Now find $AD$ from my second equation. Then use it in the first equation, to find $x$.
– Andrei
Nov 27 at 21:59
From $frac{AD}{sin 52^circ}=dfrac{AC}{sin angle{ADC}}$, do we get that $dfrac{AD}{sin 52^circ}=dfrac{11}{sin 116^circ}$?
– Enzo
Nov 27 at 21:51
From $frac{AD}{sin 52^circ}=dfrac{AC}{sin angle{ADC}}$, do we get that $dfrac{AD}{sin 52^circ}=dfrac{11}{sin 116^circ}$?
– Enzo
Nov 27 at 21:51
No. What's the $ADC$ angle? If you know it, you can get $AD$.
– Andrei
Nov 27 at 21:54
No. What's the $ADC$ angle? If you know it, you can get $AD$.
– Andrei
Nov 27 at 21:54
Isn't it $hat{ADC} = 116$?
– Enzo
Nov 27 at 21:58
Isn't it $hat{ADC} = 116$?
– Enzo
Nov 27 at 21:58
Correct. Now find $AD$ from my second equation. Then use it in the first equation, to find $x$.
– Andrei
Nov 27 at 21:59
Correct. Now find $AD$ from my second equation. Then use it in the first equation, to find $x$.
– Andrei
Nov 27 at 21:59
add a comment |
up vote
0
down vote
Knowing $angle ABD$ and $angle BAD$ you can solve for $angle ADB$ $$angle ADB=180°-26°-90°=64°$$ The angles $angle ADB$ and $angle ADC$ are supplementary, so $angle ADC=116°$. Knowing angles $angle ADC, angle ACD$, and the length of $AC$, the law of sines can be used to solve for the length of $AD$.
$$frac{11}{sin(116)}=frac{AD}{sin(52)}Rightarrow AD=frac{11sin(52)}{sin(116)}approx9,64$$ The law of sines can be used again to find $x$. $$frac{9.64}{sin(26)}=frac{x}{sin(90)}rightarrow x=frac{9.64sin(90)}{sin(26)}$$ $x$ is 22.
That is how I would do it. Sorry about the format, I am not familiar with the equation makers.
edited Nov 27 at 23:35
Dr. Mathva
926315
answered Nov 27 at 22:34
math818
33
add a comment |
up vote
0
down vote
Knowing $angle ABD$ and $angle BAD$ you can solve for $angle ADB$ $$angle ADB=180°-26°-90°=64°$$ The angles $angle ADB$ and $angle ADC$ are supplementary, so $angle ADC=116°$. Knowing angles $angle ADC, angle ACD$, and the length of $AC$, the law of sines can be used to solve for the length of $AD$.
$$frac{11}{sin(116)}=frac{AD}{sin(52)}Rightarrow AD=frac{11sin(52)}{sin(116)}approx9,64$$ The law of sines can be used again to find $x$. $$frac{9.64}{sin(26)}=frac{x}{sin(90)}rightarrow x=frac{9.64sin(90)}{sin(26)}$$ $x$ is 22.
That is how I would do it. Sorry about the format, I am not familiar with the equation makers.
edited Nov 27 at 23:35
Dr. Mathva
926315
answered Nov 27 at 22:34
math818
33
add a comment |
up vote
0
down vote
up vote
0
down vote
Knowing $angle ABD$ and $angle BAD$ you can solve for $angle ADB$ $$angle ADB=180°-26°-90°=64°$$ The angles $angle ADB$ and $angle ADC$ are supplementary, so $angle ADC=116°$. Knowing angles $angle ADC, angle ACD$, and the length of $AC$, the law of sines can be used to solve for the length of $AD$.
$$frac{11}{sin(116)}=frac{AD}{sin(52)}Rightarrow AD=frac{11sin(52)}{sin(116)}approx9,64$$ The law of sines can be used again to find $x$. $$frac{9.64}{sin(26)}=frac{x}{sin(90)}rightarrow x=frac{9.64sin(90)}{sin(26)}$$ $x$ is 22.
That is how I would do it. Sorry about the format, I am not familiar with the equation makers.
edited Nov 27 at 23:35
Dr. Mathva
926315
answered Nov 27 at 22:34
math818
33
Knowing $angle ABD$ and $angle BAD$ you can solve for $angle ADB$ $$angle ADB=180°-26°-90°=64°$$ The angles $angle ADB$ and $angle ADC$ are supplementary, so $angle ADC=116°$. Knowing angles $angle ADC, angle ACD$, and the length of $AC$, the law of sines can be used to solve for the length of $AD$.
$$frac{11}{sin(116)}=frac{AD}{sin(52)}Rightarrow AD=frac{11sin(52)}{sin(116)}approx9,64$$ The law of sines can be used again to find $x$. $$frac{9.64}{sin(26)}=frac{x}{sin(90)}rightarrow x=frac{9.64sin(90)}{sin(26)}$$ $x$ is 22.
That is how I would do it. Sorry about the format, I am not familiar with the equation makers.
edited Nov 27 at 23:35
Dr. Mathva
926315
answered Nov 27 at 22:34
math818
33
edited Nov 27 at 23:35
Dr. Mathva
926315
edited Nov 27 at 23:35
Dr. Mathva
926315
edited Nov 27 at 23:35
Dr. Mathva
926315
926315
answered Nov 27 at 22:34
math818
33
answered Nov 27 at 22:34
math818
33
answered Nov 27 at 22:34
math818
33
33
add a comment |
add a comment |
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1
You can draw a circle around triangle any time, but it does not necesery lead you to the solution.
– greedoid
Nov 27 at 20:49
2
I would use the word "inscribe" and not "convert" (i.e. inscribe the triangle in the circle). While there isn't anything wrong with it, does it really help you get to a solution? My guess would be no, but always open to new ideas.
– Aditya Dua
Nov 27 at 20:52
Hints: What are the internal angles of a triangle? What's the sum of angles in a straight line?
– Jam
Nov 27 at 20:56
Oh so, instead of directly solving the question, I need your dear assistance to change my perspective because I'm really having issues whenever I attempt to solve a question in triangles. For instance, doing what would make the question clear? I also found all angles.
– Enzo
Nov 27 at 20:59
2
@Jam Sure thing! I know Sine's theorem which states that $dfrac{a}{sin A} = dfrac{b}{sin A} = dfrac{c}{sin C}$. However, I'm also looking for strategy/method that makes it more clear than it is in this situtation.
– Enzo
Nov 27 at 21:04