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.

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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.

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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.
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.
it this the answer to number 1?

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

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