Trigonometry Modelling












0














I have another question I'm stuck on and have literally no clue to start. It's to do with trigonometry and bearings and I am horrible at worded questions.



"A jet ski travels 200m in a straight line on a bearing of 200°, then 600m in a straight line on a bearing of 060°. Calculate the distance the jet ski must travel, to the nearest m, and the bearing on which it needs to travel to return directly to its start point."



What I've done so far is constructed the triangle, but from there I'm absolutely clueless as to what I need to do.



enter image description here



Once again, thank you all.










share|cite|improve this question









New contributor




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




















  • Idea: convert the lines and distances to vectors, and add 'em up! You can put the origin at the starting point.
    – Matti P.
    Jan 4 at 12:31












  • @MattiP. I'm assuming this is an IGCSE question. If it is, the unit on vectors is after the unit on trigonometry and bearings, so the OP might not be able to use your method.
    – Toby Mak
    Jan 4 at 13:31
















0














I have another question I'm stuck on and have literally no clue to start. It's to do with trigonometry and bearings and I am horrible at worded questions.



"A jet ski travels 200m in a straight line on a bearing of 200°, then 600m in a straight line on a bearing of 060°. Calculate the distance the jet ski must travel, to the nearest m, and the bearing on which it needs to travel to return directly to its start point."



What I've done so far is constructed the triangle, but from there I'm absolutely clueless as to what I need to do.



enter image description here



Once again, thank you all.










share|cite|improve this question









New contributor




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




















  • Idea: convert the lines and distances to vectors, and add 'em up! You can put the origin at the starting point.
    – Matti P.
    Jan 4 at 12:31












  • @MattiP. I'm assuming this is an IGCSE question. If it is, the unit on vectors is after the unit on trigonometry and bearings, so the OP might not be able to use your method.
    – Toby Mak
    Jan 4 at 13:31














0












0








0







I have another question I'm stuck on and have literally no clue to start. It's to do with trigonometry and bearings and I am horrible at worded questions.



"A jet ski travels 200m in a straight line on a bearing of 200°, then 600m in a straight line on a bearing of 060°. Calculate the distance the jet ski must travel, to the nearest m, and the bearing on which it needs to travel to return directly to its start point."



What I've done so far is constructed the triangle, but from there I'm absolutely clueless as to what I need to do.



enter image description here



Once again, thank you all.










share|cite|improve this question









New contributor




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











I have another question I'm stuck on and have literally no clue to start. It's to do with trigonometry and bearings and I am horrible at worded questions.



"A jet ski travels 200m in a straight line on a bearing of 200°, then 600m in a straight line on a bearing of 060°. Calculate the distance the jet ski must travel, to the nearest m, and the bearing on which it needs to travel to return directly to its start point."



What I've done so far is constructed the triangle, but from there I'm absolutely clueless as to what I need to do.



enter image description here



Once again, thank you all.







trigonometry word-problem






share|cite|improve this question









New contributor




Jia Xuan Ng 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




Jia Xuan Ng 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




share|cite|improve this question








edited Jan 4 at 13:05









N. F. Taussig

43.6k93355




43.6k93355






New contributor




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









asked Jan 4 at 12:13









Jia Xuan NgJia Xuan Ng

51




51




New contributor




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





New contributor





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






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












  • Idea: convert the lines and distances to vectors, and add 'em up! You can put the origin at the starting point.
    – Matti P.
    Jan 4 at 12:31












  • @MattiP. I'm assuming this is an IGCSE question. If it is, the unit on vectors is after the unit on trigonometry and bearings, so the OP might not be able to use your method.
    – Toby Mak
    Jan 4 at 13:31


















  • Idea: convert the lines and distances to vectors, and add 'em up! You can put the origin at the starting point.
    – Matti P.
    Jan 4 at 12:31












  • @MattiP. I'm assuming this is an IGCSE question. If it is, the unit on vectors is after the unit on trigonometry and bearings, so the OP might not be able to use your method.
    – Toby Mak
    Jan 4 at 13:31
















Idea: convert the lines and distances to vectors, and add 'em up! You can put the origin at the starting point.
– Matti P.
Jan 4 at 12:31






Idea: convert the lines and distances to vectors, and add 'em up! You can put the origin at the starting point.
– Matti P.
Jan 4 at 12:31














@MattiP. I'm assuming this is an IGCSE question. If it is, the unit on vectors is after the unit on trigonometry and bearings, so the OP might not be able to use your method.
– Toby Mak
Jan 4 at 13:31




@MattiP. I'm assuming this is an IGCSE question. If it is, the unit on vectors is after the unit on trigonometry and bearings, so the OP might not be able to use your method.
– Toby Mak
Jan 4 at 13:31










1 Answer
1






active

oldest

votes


















3














enter image description here



(DB, EA, and FC are all parallel)



If only we had $angle ABC$, we could use the cosine rule to find $AC$! Well, that's exactly what we're going to do:



$$angle EAB = 160º text{(reflex angles)}$$
$$angle DBA = 20º text{(alternate angles)}$$
$$ABC = 40º$$



Now, use the cosine rule:
$$AC^2 = 200^2 + 600^2 - 2(200)(600) cos 40º$$
$$AC = sqrt{200^2 + 600^2 - 2(200)(600) cos 40º}$$
$$= 465 text{(3 s.f)}$$



Now for part $2$, the bearing of $CA$ is just $360º - angle FCA$. However, $angle DBC$ and $angle FCB$ are corresponding angles, so $angle FCB = 120º$.



If you just work out $angle ACB$ (either sine rule or cosine rule works with $AC$ known), you can get the answer.






share|cite|improve this answer





















  • What software are you using? GeoGebra?
    – Lucas Henrique
    Jan 4 at 13:33










  • @LucasHenrique Yep. I also haven't used Paint before.
    – Toby Mak
    Jan 4 at 13:34











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
});


}
});






Jia Xuan Ng is a new contributor. Be nice, and check out our Code of Conduct.










draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061589%2ftrigonometry-modelling%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









3














enter image description here



(DB, EA, and FC are all parallel)



If only we had $angle ABC$, we could use the cosine rule to find $AC$! Well, that's exactly what we're going to do:



$$angle EAB = 160º text{(reflex angles)}$$
$$angle DBA = 20º text{(alternate angles)}$$
$$ABC = 40º$$



Now, use the cosine rule:
$$AC^2 = 200^2 + 600^2 - 2(200)(600) cos 40º$$
$$AC = sqrt{200^2 + 600^2 - 2(200)(600) cos 40º}$$
$$= 465 text{(3 s.f)}$$



Now for part $2$, the bearing of $CA$ is just $360º - angle FCA$. However, $angle DBC$ and $angle FCB$ are corresponding angles, so $angle FCB = 120º$.



If you just work out $angle ACB$ (either sine rule or cosine rule works with $AC$ known), you can get the answer.






share|cite|improve this answer





















  • What software are you using? GeoGebra?
    – Lucas Henrique
    Jan 4 at 13:33










  • @LucasHenrique Yep. I also haven't used Paint before.
    – Toby Mak
    Jan 4 at 13:34
















3














enter image description here



(DB, EA, and FC are all parallel)



If only we had $angle ABC$, we could use the cosine rule to find $AC$! Well, that's exactly what we're going to do:



$$angle EAB = 160º text{(reflex angles)}$$
$$angle DBA = 20º text{(alternate angles)}$$
$$ABC = 40º$$



Now, use the cosine rule:
$$AC^2 = 200^2 + 600^2 - 2(200)(600) cos 40º$$
$$AC = sqrt{200^2 + 600^2 - 2(200)(600) cos 40º}$$
$$= 465 text{(3 s.f)}$$



Now for part $2$, the bearing of $CA$ is just $360º - angle FCA$. However, $angle DBC$ and $angle FCB$ are corresponding angles, so $angle FCB = 120º$.



If you just work out $angle ACB$ (either sine rule or cosine rule works with $AC$ known), you can get the answer.






share|cite|improve this answer





















  • What software are you using? GeoGebra?
    – Lucas Henrique
    Jan 4 at 13:33










  • @LucasHenrique Yep. I also haven't used Paint before.
    – Toby Mak
    Jan 4 at 13:34














3












3








3






enter image description here



(DB, EA, and FC are all parallel)



If only we had $angle ABC$, we could use the cosine rule to find $AC$! Well, that's exactly what we're going to do:



$$angle EAB = 160º text{(reflex angles)}$$
$$angle DBA = 20º text{(alternate angles)}$$
$$ABC = 40º$$



Now, use the cosine rule:
$$AC^2 = 200^2 + 600^2 - 2(200)(600) cos 40º$$
$$AC = sqrt{200^2 + 600^2 - 2(200)(600) cos 40º}$$
$$= 465 text{(3 s.f)}$$



Now for part $2$, the bearing of $CA$ is just $360º - angle FCA$. However, $angle DBC$ and $angle FCB$ are corresponding angles, so $angle FCB = 120º$.



If you just work out $angle ACB$ (either sine rule or cosine rule works with $AC$ known), you can get the answer.






share|cite|improve this answer












enter image description here



(DB, EA, and FC are all parallel)



If only we had $angle ABC$, we could use the cosine rule to find $AC$! Well, that's exactly what we're going to do:



$$angle EAB = 160º text{(reflex angles)}$$
$$angle DBA = 20º text{(alternate angles)}$$
$$ABC = 40º$$



Now, use the cosine rule:
$$AC^2 = 200^2 + 600^2 - 2(200)(600) cos 40º$$
$$AC = sqrt{200^2 + 600^2 - 2(200)(600) cos 40º}$$
$$= 465 text{(3 s.f)}$$



Now for part $2$, the bearing of $CA$ is just $360º - angle FCA$. However, $angle DBC$ and $angle FCB$ are corresponding angles, so $angle FCB = 120º$.



If you just work out $angle ACB$ (either sine rule or cosine rule works with $AC$ known), you can get the answer.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 4 at 13:29









Toby MakToby Mak

3,37811128




3,37811128












  • What software are you using? GeoGebra?
    – Lucas Henrique
    Jan 4 at 13:33










  • @LucasHenrique Yep. I also haven't used Paint before.
    – Toby Mak
    Jan 4 at 13:34


















  • What software are you using? GeoGebra?
    – Lucas Henrique
    Jan 4 at 13:33










  • @LucasHenrique Yep. I also haven't used Paint before.
    – Toby Mak
    Jan 4 at 13:34
















What software are you using? GeoGebra?
– Lucas Henrique
Jan 4 at 13:33




What software are you using? GeoGebra?
– Lucas Henrique
Jan 4 at 13:33












@LucasHenrique Yep. I also haven't used Paint before.
– Toby Mak
Jan 4 at 13:34




@LucasHenrique Yep. I also haven't used Paint before.
– Toby Mak
Jan 4 at 13:34










Jia Xuan Ng is a new contributor. Be nice, and check out our Code of Conduct.










draft saved

draft discarded


















Jia Xuan Ng is a new contributor. Be nice, and check out our Code of Conduct.













Jia Xuan Ng is a new contributor. Be nice, and check out our Code of Conduct.












Jia Xuan Ng is a new contributor. Be nice, and check out our Code of Conduct.
















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.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061589%2ftrigonometry-modelling%23new-answer', 'question_page');
}
);

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







Popular posts from this blog

1300-talet

1300-talet

Display a custom attribute below product name in the front-end Magento 1.9.3.8