How do we solve for $x$ using law of sines?
up vote
2
down vote
favorite
How do we solve for $x$ using the law of sines?
Here's my attempt:
$$angle BDC = 180- 30 - 12 = 138^circ$$
So we have that
$$dfrac{sin 30 }{|DC|} = dfrac{sin 12}{|DB|} = dfrac{sin 138}{|BC|} $$
For $triangle{ABD}$
$$dfrac{sin 18 }{|AD|} = dfrac{sin 24}{|DB|}$$
And what I need to evaluate is
$$dfrac{sin x }{|DC|} = ? $$
Can you help me take it from here?
trigonometry triangle
edited Nov 28 at 22:58
clathratus
2,735326
asked Nov 28 at 21:14
Hamilton
1838
add a comment |
up vote
2
down vote
favorite
How do we solve for $x$ using the law of sines?
Here's my attempt:
$$angle BDC = 180- 30 - 12 = 138^circ$$
So we have that
$$dfrac{sin 30 }{|DC|} = dfrac{sin 12}{|DB|} = dfrac{sin 138}{|BC|} $$
For $triangle{ABD}$
$$dfrac{sin 18 }{|AD|} = dfrac{sin 24}{|DB|}$$
And what I need to evaluate is
$$dfrac{sin x }{|DC|} = ? $$
Can you help me take it from here?
trigonometry triangle
edited Nov 28 at 22:58
clathratus
2,735326
asked Nov 28 at 21:14
Hamilton
1838
What else is valid for the triangle?
– greedoid
Nov 28 at 21:18
observe that $angle BDA =138^circ$
– Vasya
Nov 28 at 21:31
You can use Trigonometric form of Ceva's theorem to find $x$.
– Muralidharan
Nov 28 at 21:43
note that $180-24-18=138$, thus $angle ADB=138$. This gives $$angle ADC=84$$
– clathratus
Nov 28 at 21:50
I want to directly solve for $x$ using Sine law. Can anyone provide an answer if that's possible?
– Hamilton
Nov 29 at 13:25
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
How do we solve for $x$ using the law of sines?
Here's my attempt:
$$angle BDC = 180- 30 - 12 = 138^circ$$
So we have that
$$dfrac{sin 30 }{|DC|} = dfrac{sin 12}{|DB|} = dfrac{sin 138}{|BC|} $$
For $triangle{ABD}$
$$dfrac{sin 18 }{|AD|} = dfrac{sin 24}{|DB|}$$
And what I need to evaluate is
$$dfrac{sin x }{|DC|} = ? $$
Can you help me take it from here?
trigonometry triangle
edited Nov 28 at 22:58
clathratus
2,735326
asked Nov 28 at 21:14
Hamilton
1838
How do we solve for $x$ using the law of sines?
Here's my attempt:
$$angle BDC = 180- 30 - 12 = 138^circ$$
So we have that
$$dfrac{sin 30 }{|DC|} = dfrac{sin 12}{|DB|} = dfrac{sin 138}{|BC|} $$
For $triangle{ABD}$
$$dfrac{sin 18 }{|AD|} = dfrac{sin 24}{|DB|}$$
And what I need to evaluate is
$$dfrac{sin x }{|DC|} = ? $$
Can you help me take it from here?
trigonometry triangle
trigonometry triangle
edited Nov 28 at 22:58
clathratus
2,735326
asked Nov 28 at 21:14
Hamilton
1838
edited Nov 28 at 22:58
clathratus
2,735326
asked Nov 28 at 21:14
Hamilton
1838
edited Nov 28 at 22:58
clathratus
2,735326
edited Nov 28 at 22:58
clathratus
2,735326
edited Nov 28 at 22:58
clathratus
2,735326
2,735326
asked Nov 28 at 21:14
Hamilton
1838
asked Nov 28 at 21:14
Hamilton
1838
asked Nov 28 at 21:14
Hamilton
1838
1838
What else is valid for the triangle?
– greedoid
Nov 28 at 21:18
observe that $angle BDA =138^circ$
– Vasya
Nov 28 at 21:31
You can use Trigonometric form of Ceva's theorem to find $x$.
– Muralidharan
Nov 28 at 21:43
note that $180-24-18=138$, thus $angle ADB=138$. This gives $$angle ADC=84$$
– clathratus
Nov 28 at 21:50
I want to directly solve for $x$ using Sine law. Can anyone provide an answer if that's possible?
– Hamilton
Nov 29 at 13:25
add a comment |
What else is valid for the triangle?
– greedoid
Nov 28 at 21:18
observe that $angle BDA =138^circ$
– Vasya
Nov 28 at 21:31
You can use Trigonometric form of Ceva's theorem to find $x$.
– Muralidharan
Nov 28 at 21:43
note that $180-24-18=138$, thus $angle ADB=138$. This gives $$angle ADC=84$$
– clathratus
Nov 28 at 21:50
I want to directly solve for $x$ using Sine law. Can anyone provide an answer if that's possible?
– Hamilton
Nov 29 at 13:25
What else is valid for the triangle?
– greedoid
Nov 28 at 21:18
What else is valid for the triangle?
– greedoid
Nov 28 at 21:18
observe that $angle BDA =138^circ$
– Vasya
Nov 28 at 21:31
observe that $angle BDA =138^circ$
– Vasya
Nov 28 at 21:31
You can use Trigonometric form of Ceva's theorem to find $x$.
– Muralidharan
Nov 28 at 21:43
You can use Trigonometric form of Ceva's theorem to find $x$.
– Muralidharan
Nov 28 at 21:43
note that $180-24-18=138$, thus $angle ADB=138$. This gives $$angle ADC=84$$
– clathratus
Nov 28 at 21:50
note that $180-24-18=138$, thus $angle ADB=138$. This gives $$angle ADC=84$$
– clathratus
Nov 28 at 21:50
I want to directly solve for $x$ using Sine law. Can anyone provide an answer if that's possible?
– Hamilton
Nov 29 at 13:25
I want to directly solve for $x$ using Sine law. Can anyone provide an answer if that's possible?
– Hamilton
Nov 29 at 13:25
add a comment |
2 Answers
2
active
oldest
votes
up vote
1
down vote
This works if you know what $|BC|$ and $|AC|$ are.
$$frac{sin(x+24)}{|BC|}=frac{sin48}{|AC|}$$
$$sin(x+24)=frac{|BC|sin48}{|AC|}$$
$$x+24=arcsinbigg(frac{|BC|sin48}{|AC|}bigg)$$
$$x=arcsinbigg(frac{|BC|sin48}{|AC|}bigg)-24$$
answered Nov 28 at 21:57
clathratus
2,735326
add a comment |
up vote
0
down vote
Recall that the angles of a triangle must add up to 180°. From this we can conclude that angle $CDB$ measures 138° and angle $BDA$ measures 138°. Therefore angle $ADC$ measures 84°. Now, if we let $y$ be the measure of angle $DCA$ (in degrees), we have the following system of equations.
$$ begin{array}{rcr} x + y + 84 & = & 180 \ x + y + 84 & = & 180 end{array} $$
So I want to say there will be infinitely many solutions... apparently there is some freedom in choosing the sides, as the other answer has hinted. But not 100% sure. Anyone else want to weigh in?
answered Nov 29 at 11:40
Nikifuj908
635
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3017718%2fhow-do-we-solve-for-x-using-law-of-sines%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
This works if you know what $|BC|$ and $|AC|$ are.
$$frac{sin(x+24)}{|BC|}=frac{sin48}{|AC|}$$
$$sin(x+24)=frac{|BC|sin48}{|AC|}$$
$$x+24=arcsinbigg(frac{|BC|sin48}{|AC|}bigg)$$
$$x=arcsinbigg(frac{|BC|sin48}{|AC|}bigg)-24$$
answered Nov 28 at 21:57
clathratus
2,735326
add a comment |
up vote
1
down vote
This works if you know what $|BC|$ and $|AC|$ are.
$$frac{sin(x+24)}{|BC|}=frac{sin48}{|AC|}$$
$$sin(x+24)=frac{|BC|sin48}{|AC|}$$
$$x+24=arcsinbigg(frac{|BC|sin48}{|AC|}bigg)$$
$$x=arcsinbigg(frac{|BC|sin48}{|AC|}bigg)-24$$
answered Nov 28 at 21:57
clathratus
2,735326
add a comment |
up vote
1
down vote
up vote
1
down vote
This works if you know what $|BC|$ and $|AC|$ are.
$$frac{sin(x+24)}{|BC|}=frac{sin48}{|AC|}$$
$$sin(x+24)=frac{|BC|sin48}{|AC|}$$
$$x+24=arcsinbigg(frac{|BC|sin48}{|AC|}bigg)$$
$$x=arcsinbigg(frac{|BC|sin48}{|AC|}bigg)-24$$
answered Nov 28 at 21:57
clathratus
2,735326
This works if you know what $|BC|$ and $|AC|$ are.
$$frac{sin(x+24)}{|BC|}=frac{sin48}{|AC|}$$
$$sin(x+24)=frac{|BC|sin48}{|AC|}$$
$$x+24=arcsinbigg(frac{|BC|sin48}{|AC|}bigg)$$
$$x=arcsinbigg(frac{|BC|sin48}{|AC|}bigg)-24$$
answered Nov 28 at 21:57
clathratus
2,735326
answered Nov 28 at 21:57
clathratus
2,735326
answered Nov 28 at 21:57
clathratus
2,735326
answered Nov 28 at 21:57
clathratus
2,735326
2,735326
add a comment |
add a comment |
up vote
0
down vote
Recall that the angles of a triangle must add up to 180°. From this we can conclude that angle $CDB$ measures 138° and angle $BDA$ measures 138°. Therefore angle $ADC$ measures 84°. Now, if we let $y$ be the measure of angle $DCA$ (in degrees), we have the following system of equations.
$$ begin{array}{rcr} x + y + 84 & = & 180 \ x + y + 84 & = & 180 end{array} $$
So I want to say there will be infinitely many solutions... apparently there is some freedom in choosing the sides, as the other answer has hinted. But not 100% sure. Anyone else want to weigh in?
answered Nov 29 at 11:40
Nikifuj908
635
add a comment |
up vote
0
down vote
Recall that the angles of a triangle must add up to 180°. From this we can conclude that angle $CDB$ measures 138° and angle $BDA$ measures 138°. Therefore angle $ADC$ measures 84°. Now, if we let $y$ be the measure of angle $DCA$ (in degrees), we have the following system of equations.
$$ begin{array}{rcr} x + y + 84 & = & 180 \ x + y + 84 & = & 180 end{array} $$
So I want to say there will be infinitely many solutions... apparently there is some freedom in choosing the sides, as the other answer has hinted. But not 100% sure. Anyone else want to weigh in?
answered Nov 29 at 11:40
Nikifuj908
635
add a comment |
up vote
0
down vote
up vote
0
down vote
Recall that the angles of a triangle must add up to 180°. From this we can conclude that angle $CDB$ measures 138° and angle $BDA$ measures 138°. Therefore angle $ADC$ measures 84°. Now, if we let $y$ be the measure of angle $DCA$ (in degrees), we have the following system of equations.
$$ begin{array}{rcr} x + y + 84 & = & 180 \ x + y + 84 & = & 180 end{array} $$
So I want to say there will be infinitely many solutions... apparently there is some freedom in choosing the sides, as the other answer has hinted. But not 100% sure. Anyone else want to weigh in?
answered Nov 29 at 11:40
Nikifuj908
635
Recall that the angles of a triangle must add up to 180°. From this we can conclude that angle $CDB$ measures 138° and angle $BDA$ measures 138°. Therefore angle $ADC$ measures 84°. Now, if we let $y$ be the measure of angle $DCA$ (in degrees), we have the following system of equations.
$$ begin{array}{rcr} x + y + 84 & = & 180 \ x + y + 84 & = & 180 end{array} $$
So I want to say there will be infinitely many solutions... apparently there is some freedom in choosing the sides, as the other answer has hinted. But not 100% sure. Anyone else want to weigh in?
answered Nov 29 at 11:40
Nikifuj908
635
answered Nov 29 at 11:40
Nikifuj908
635
answered Nov 29 at 11:40
Nikifuj908
635
answered Nov 29 at 11:40
Nikifuj908
635
635
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3017718%2fhow-do-we-solve-for-x-using-law-of-sines%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
What else is valid for the triangle?
– greedoid
Nov 28 at 21:18
observe that $angle BDA =138^circ$
– Vasya
Nov 28 at 21:31
You can use Trigonometric form of Ceva's theorem to find $x$.
– Muralidharan
Nov 28 at 21:43
note that $180-24-18=138$, thus $angle ADB=138$. This gives $$angle ADC=84$$
– clathratus
Nov 28 at 21:50
I want to directly solve for $x$ using Sine law. Can anyone provide an answer if that's possible?
– Hamilton
Nov 29 at 13:25