A beautiful geometric problem based on Sine and Cosine rule

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(Edited)

Hello math bugs(🐞) and (🐝)
I hope you are strong and stout and doin well in life.

Well come to another beautiful geometric problem based on triangle. You have already seen it in cover photo. There are a few ways to solve it. But if we don't wanna take help of a calculator, we should use trigonometry. Yeah we gonna use Sine rule and Cosine rule to find out BC.
Consider the following figure. Here straight ∠BDC comprises of two angles namely ∠ADB and ∠ADC. So there are supplementary i.e sum of them will be 180°. So, we let's say ∠ADC=θ ∠ADB=(180º-θ).Check details:

The figure can be decided into two half as you can see in the following figure. Now time to use Sine rule in both of the triangle and thus we get two equation. Further solving it we can have Ratio of BD and CD. It is given by BD : CD = 2 : 1. Check details: For details tap SINE RULE

Let's CD and BD be y cm and 2y cm respectively as BD : CD = 2 : 1 proved above. Before applying Cosine rule check the following details of data we have right now:

In the following two triangle,now, we gonna use derived part of Cosine rule.You may have difficulty; I suggest you to go through derivation part of Cosine rule. The link is at the bottom of the following figure. For details tap COSINE RULE

Now the work is done.You have to solve the following two equations. I have done it skipping a few steps as I was running out of space. You can try solving it in your way. So we got x = 150 cm. We can find the value of x in other simple way also but from there getting value of y would a tough task with out using calculator. That's why I chose this process. Now putting the value of x in any of the equation we can find value of y also. Ignore my calculation ; a fews steps are ignored. So we now have y= 50√7.

But we need value of BD. We can see value of BD is three times of y So required answer (BC or 3y) is 150√7 as you can see it in the following figure:

Please ignore if you find any silly mistakes. All the figures are used here are prepared by me and they took huge time. So editing again is very time consuming and boaring also. Sorry for that.

I found a mistake later (BD≠3y) it will be BC=3y= 150√7

I hope you have found my articles effort full, please don't forget to share and feel free to make a comment if you find any mistake or for more information.

Thanks you so much for visiting and supporting.

Have a good day

All is well

Regards: @meta007

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14 comments
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You are saviour of every student here! Have seen you explain things simply.

Awesome mate. Keep it up. !LUV

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Thanks man for the complement, visit and support.It means a lot.

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This will really help the mathematics students and all students as questions concerning the sine and cosine rules always come out in exams

That's a beautiful explanation mate

Thanks

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Thanks man for the compliment and your visit.
It is really encouraging for me.

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Beautiful! I read through it but as you know already, it went over my cabeza. 🤣 Oh man, this is so sad 😊

Do yo Math and Geometry coaching online!?

!POB

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Hello acgalarza

I am very sorry for you trouble. Actually things depends on our liking to them. As this is a little bit higer than basic concepts. It needs more and more practise and clear knowledge of basics. Once it's done you will be all okay.. My next post will about algebra which must interest you.

No I haven't started teaching online. All what I do is teaching school students offline. When I joined hive, my moto was to post mathematics concepts. I am continuing with it and I can see people's support is always there. I don't know if any kind who preparing for exam, notices my post. If They do I'll more than happy.

Thanks man for you always visit and making a comment. It encourages me to work hard.

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You are right, interest plays a huge role in learning anything in life. Yes, Algebra is nice, although at my age and after so many years after school - it remains a challenge to me. A good challenge.

Here is an idea for you. Maybe you should try to do videos about your material in 3Speak. You could walk us through the process. I believe your posts could gain more attention...and votes too, while at the same time reaching more people. What do you think?

!CCC
!POB
!PGM

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You are right. I had a thought about it.Now I make post after 5 or 6 days.Whenever I got free time I try to frame my pictures. At moment time to make a video is not possible cause a can not be made in installment.I have taken your advise. I'll do it in future.

Thanks man for your valuable feed back.

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Thanks for your contribution to the STEMsocial community. Feel free to join us on discord to get to know the rest of us!

Please consider delegating to the @stemsocial account (85% of the curation rewards are returned).

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Very detailed!
I got a little dizzy though seeing the expressions. 😅
Hope this will help someone else out there!

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😂 I am sorry for for making you dizzy.Your always visit is appreciable.Thanks wittyzel.

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