PLEASE HELP! I'm really stuck! ABC is a triangle. AC = 8.6cm BC = 5.7cm and angle ABC = 110 degrees. Calculate the area of the triangle giving your answer to 3 significant figures

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thank you :)

Posted Tue 12th June, 2012 @ 19:39 by Millie

23 Answers

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well!! this is how u do the question !!

Draw a random triangle (when i mean random i mean not a right-angled triangle)

label the edges A, B, C !!

Then put the angle in !!

Now for the area of a triangle to work u must have a SAS (Side - angle-side) meaning a angle between two sides !!

You can see that u dont have that, so use the sine rule to work out BAC and from that do 180 minus (your worked out angle + 110)  this will give you the angle ACB !!

Then you can sub in the values into 0.5 x a x b x sinC

Now to show you what i mean !!!

Now above is a diagram i drew to help u visualize this !!! (P.S i hope u can see this !!!)

Now we have to work out BAC or in other words !!

So you use the sine rule :

sin x = (5.7xsin110 ) / 8.6

     x  = Sin^-1 (ANS   =    38.5 to 3 sig figs (keep the value on your calculator!!)

Now we have to work out BCA or angle Y !!

To do this you do the following:

y =180 - (your answer on your calculator + 110)====> angles in a triangle equal 180 degrees

y = 31.5 degrees to 3 sig figs (again keep your calculator answer on your calculator !!)

Finally you can work out the area by subbing in angle Y, n the two other sides into the equation :

0.5 x a x b x sinC

so this is how it is::

0.5 x 8.6 x 5.7 x sin (your calculator answer for BCA) = 12.79829599

                                                                           = 12.8cm^2    (3 sig figs !!!)

I think this is right and i hope i have helped !!

Answered Tue 12th June, 2012 @ 20:05 by Braniac
Edited by Braniac on Tue 12th June, 2012 @ 20:17
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You need to use the sine rule :)

I'm not gonna give you the answer because you should try doing it yourself :D

The formula is:  Area=1/2absinC

a - being one of the side

b - being the other side

C - being the angle 

Hope I helped!! :D

Answered Tue 12th June, 2012 @ 19:45 by manga fan =D
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what type of triangle is it??? is 8.6 the longest side???

Answered Tue 12th June, 2012 @ 19:46 by Muzz :P
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Thank you, although i tried both of those things but because i don't have angle C i cant do the area formula and because i dont have side c, i cant do the sine rule either :S

Answered Tue 12th June, 2012 @ 19:47 by Millie
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its congruent i think and i don't know because i only have 2 sides given ;/

Answered Tue 12th June, 2012 @ 19:48 by Millie
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have you tried the cosine rule???

Answered Tue 12th June, 2012 @ 19:48 by Muzz :P
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yeah :/ but no luck as to find the angle with the cosine rule i need side AB and to find the length of side AB i need the angle C :S

Answered Tue 12th June, 2012 @ 19:50 by Millie
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Oh sorry ... I didn't realise ^^

How about trying to find out with this formula:

a/sinA = b/sinB = c/sinC

/ meaning divide or over

Hope you know what I mean :S

And then use the sine rule

Answered Tue 12th June, 2012 @ 19:51 by manga fan =D
Edited by manga fan =D on Tue 12th June, 2012 @ 19:52
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sorry if i wasn't clear enough, when i said 'side c' that is the same as the missing side 'AB' :) 

Answered Tue 12th June, 2012 @ 19:52 by Millie
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okay, i'll try that :) thanks :D

Answered Tue 12th June, 2012 @ 19:53 by Millie
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ooh actually i just realised that as i dont know angle's a and b, thats gonna be very difficult...

Answered Tue 12th June, 2012 @ 19:54 by Millie
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Whaaaaaaat?! ... -_-" ... what kind of question is that! :P

Answered Tue 12th June, 2012 @ 19:59 by manga fan =D
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i know right! its ridiculous :/

Answered Tue 12th June, 2012 @ 20:02 by Millie
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lol like my pic if u can c it XD i had to draw it on paint XD

Answered Tue 12th June, 2012 @ 20:06 by Braniac
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Muzz just have a look at wot i done i think i explained how i did it !!

Answered Tue 12th June, 2012 @ 20:08 by Braniac
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:O ... this is amazing beelal!!    :D

Answered Tue 12th June, 2012 @ 20:09 by manga fan =D
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hey where's my comment gone..

 and @ beelal i had a look and i think i get it now... thanks... :)

Answered Tue 12th June, 2012 @ 20:10 by Muzz :P
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lol no problem !! im glad i could help !! you just gotta remember that b4 u culd have got straight into the area of a triangle you needed to know what values you have to use first and for the cosine rule and area of triangle you need a S.A.S (a angle between two sides !!! )  =D

Answered Tue 12th June, 2012 @ 20:14 by Braniac
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it think its this

(sin110/8.6)x5.7=0.6228195277

Sin-1(ANS)= 38.5 degrees    so angle A = 38.5 degrees

Angle C= 180-(110+38.5) = 31.5 degrees

The area of the triangle is 0.5xaxbxsinC

Area= 0.5x8.6x5.7x(sin31.5)

Area= 12.8 cm squared (3sf)

Answered Tue 12th June, 2012 @ 20:15 by Amy
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@ beelal i just had a go at it and i got 15.3 i worked it out by using the sine rule and then the 1/2absinc... :/

Answered Tue 12th June, 2012 @ 20:29 by Muzz :P
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did u use the sine rule to get angle BAC in my diagram !! But then did u work out the angle BCA by doin the step:

y =180 - (your answer on your calculator + 110)====> angles in a triangle equal 180 degrees

???

becuz if u did then u shuld get my answer !!

u might have forgotten that, or u culd have used te wrong angle etc etc !!

 But hope i have solved your quesry !

Answered Tue 12th June, 2012 @ 20:32 by Braniac
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yup my bad... :( sorry....

Answered Tue 12th June, 2012 @ 20:40 by Muzz :P
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thanks everyone :) while i was offline me and my friend managed to figure it out and we used the same method as beelal and amy. thank you for all your help :D x

Answered Tue 12th June, 2012 @ 20:45 by Millie