anonymous
  • anonymous
Need help with triangle questions! Please HELP! Find the Area of Triangle ABC. 1. angle b = 25º, a = 10 mm, and c = 15 mm. 2. angle a = 42º, b = 12 cm, and c = 13 cm. 3. angle c = 100º, a = 5 in., and b = 4 in. 4. angle c = 59º, a = 25 ft, and b = 18 ft.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
are of a triangle is \[\frac{1}{2} ab sin(\theta)\] where \[\theta\] is the measure of the angle between a and b. so these are straightforward i think. first one is \[\frac{1}{2} 10 \times 15 \times sin(25)=31.7\] rounded.
anonymous
  • anonymous
i am assuming that when you say angle b you mean angle B. commonly lengths are denoted by small letters and the angles opposite them by capitals.
anonymous
  • anonymous
it this the answer to number 1?

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anonymous
  • anonymous
yes if i used my calculator correctly.
anonymous
  • anonymous
can you answer the other 3 please? I will give you a good answer for all
anonymous
  • anonymous
want me to write the next one or do you want to do it. just use the formula.
anonymous
  • anonymous
you do next one I will do last 2 if I can
anonymous
  • anonymous
ok here goes: \[\frac{1}{2}\times 12 \times 13 \times sin(42)=52.19\]
anonymous
  • anonymous
i am just using a calculator. you need one to find the sine of whatever. just make sure it is in "degree" mode. you do one and i will check.
anonymous
  • anonymous
ok I did 1/2*5*4*sin100 and got -5.063 is that right?
anonymous
  • anonymous
no you area must be positive.
anonymous
  • anonymous
i think maybe your calculator is in radian mode. let me check.
anonymous
  • anonymous
hmmm ok I am using the Ti-84 Plus calc and idk what i did wrong how do I change it?
anonymous
  • anonymous
hit "mode" and you should see the option there.
anonymous
  • anonymous
http://answers.yahoo.com/question/index?qid=20090312222055AA3FPqb
anonymous
  • anonymous
I got 9.84???
anonymous
  • anonymous
yes!
anonymous
  • anonymous
wow thanks I get it now!! Can I ask 2 more 1 for each next section then maybe I can understand it!???
anonymous
  • anonymous
sure ask away.
anonymous
  • anonymous
sweet thanks
anonymous
  • anonymous
Find the remaining sides and angles in each triangle. 1. In Triangle ABC , angle M= 38º, a = 20 cm and c = 14 cm.
anonymous
  • anonymous
i need to know (or rather you need to know) what angle is M? is it opposite a, b or c?
anonymous
  • anonymous
2. in triangle DEF, d = 24 m, e = 21 m, and f = 25 m. I will try this one Angle m is B
anonymous
  • anonymous
opposite b? ok
anonymous
  • anonymous
yeah it say m Angle B=...
anonymous
  • anonymous
so in the first one you don't know the length of the side opposite angle M = 38 yes?
anonymous
  • anonymous
yes that sounds right
anonymous
  • anonymous
because either you are supposed to use the law of sines which says \[\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}\]
anonymous
  • anonymous
or you are supposed to use the law of cosines which says \[a^2=b^2+c^2-2bc cos(A)\]
anonymous
  • anonymous
in order to use the first one (which is always easier) you need to know three out of 4 numbers in any one of those ratios. but it looks like in this case you do not. you only know two sides but not the length of the side opposite one of the angles. so you have to use the law of cosines yes?
anonymous
  • anonymous
yes!
anonymous
  • anonymous
so we will have to use \[b^2=a^2+c^2 -2ac cos(B)\]
anonymous
  • anonymous
btw this is easy to remember because it is just pythagoras. if you had a right angle it would be \[c^2=a^2+b^2\] but if it is not a right angle you have to adjust by \[-2ab cos(C)\] ok here goes: \[b^2=20^2+14^2-2\times 20 \times 14 \times cos(38)=154.7\] rounded
anonymous
  • anonymous
so \[b=\sqrt{154.1}=12.4\] rounded
anonymous
  • anonymous
at least that is what my calculator told me
anonymous
  • anonymous
ok lol that makes since
anonymous
  • anonymous
of course you are not done because you have to find all the rest.
anonymous
  • anonymous
would it make it easier if I gave you choices? CHoices: b = 12.4 cm2, A = 78.1º, C = 41.5º b = 9.8 cm2, A = 56.1º, C = 57.5º b = 12.4 cm2, A = 98.1º, C = 43.9º b = 12.4 cm2, A = 92.3º, C = 37.6º
anonymous
  • anonymous
not really. especially since we have only knocked out one answer.
anonymous
  • anonymous
you still have to find A and C
anonymous
  • anonymous
oo right ok
anonymous
  • anonymous
but do not use the law of cosines again, because now you know the side opposite one of the angles. to find angle A use \[\frac{sin(A)}{a}=\frac{sin(B)}{b}\] or \[sin(A)=\frac{a sin(B)}{b}\]
anonymous
  • anonymous
\[sin(A) = \frac{20 sin(38)}{12.4} = .993\] i think
anonymous
  • anonymous
damn i am not getting any of your answers.
anonymous
  • anonymous
sorry....
anonymous
  • anonymous
ok but i am sure this is correct. we have the 12.4 for sure. now let us find angle C \[\frac{sin(C)}{c}=\frac{sin(B)}{b}\] \[sin(C) = \frac{sin(B)}{b}\] \[sin(C) = \frac{14 sin(38)}{12.4}\] \[C=sin^{-1}(\frac{14 sin(38)}{12.4})\]
anonymous
  • anonymous
my calc gives 44.03
anonymous
  • anonymous
but don't forget that we rounded b = 12.4. maybe if we don't round we get a more exact answer.
anonymous
  • anonymous
yes i get 43.9 if i don't round for b. weird that they would give b as 12.4 but then not round to find A or C.
anonymous
  • anonymous
ok so A =43.9
anonymous
  • anonymous
no that was C A you find by subracting: 180 - 38 - 43.9=98.1
anonymous
  • anonymous
wanna try the next one?
anonymous
  • anonymous
sryy gotta go thanks for the help tho
anonymous
  • anonymous
welcome

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