## anonymous 5 years ago 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.

1. 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.

2. 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.

3. anonymous

it this the answer to number 1?

4. anonymous

yes if i used my calculator correctly.

5. anonymous

6. anonymous

want me to write the next one or do you want to do it. just use the formula.

7. anonymous

you do next one I will do last 2 if I can

8. anonymous

ok here goes: $\frac{1}{2}\times 12 \times 13 \times sin(42)=52.19$

9. 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.

10. anonymous

ok I did 1/2*5*4*sin100 and got -5.063 is that right?

11. anonymous

no you area must be positive.

12. anonymous

i think maybe your calculator is in radian mode. let me check.

13. anonymous

hmmm ok I am using the Ti-84 Plus calc and idk what i did wrong how do I change it?

14. anonymous

hit "mode" and you should see the option there.

15. anonymous
16. anonymous

I got 9.84???

17. anonymous

yes!

18. anonymous

wow thanks I get it now!! Can I ask 2 more 1 for each next section then maybe I can understand it!???

19. anonymous

20. anonymous

sweet thanks

21. anonymous

Find the remaining sides and angles in each triangle. 1. In Triangle ABC , angle M= 38º, a = 20 cm and c = 14 cm.

22. anonymous

i need to know (or rather you need to know) what angle is M? is it opposite a, b or c?

23. anonymous

2. in triangle DEF, d = 24 m, e = 21 m, and f = 25 m. I will try this one Angle m is B

24. anonymous

opposite b? ok

25. anonymous

yeah it say m Angle B=...

26. anonymous

so in the first one you don't know the length of the side opposite angle M = 38 yes?

27. anonymous

yes that sounds right

28. anonymous

because either you are supposed to use the law of sines which says $\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$

29. anonymous

or you are supposed to use the law of cosines which says $a^2=b^2+c^2-2bc cos(A)$

30. 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?

31. anonymous

yes!

32. anonymous

so we will have to use $b^2=a^2+c^2 -2ac cos(B)$

33. 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

34. anonymous

so $b=\sqrt{154.1}=12.4$ rounded

35. anonymous

at least that is what my calculator told me

36. anonymous

ok lol that makes since

37. anonymous

of course you are not done because you have to find all the rest.

38. 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

39. anonymous

not really. especially since we have only knocked out one answer.

40. anonymous

you still have to find A and C

41. anonymous

oo right ok

42. 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 $sin(A)=\frac{a sin(B)}{b}$

43. anonymous

$sin(A) = \frac{20 sin(38)}{12.4} = .993$ i think

44. anonymous

45. anonymous

sorry....

46. anonymous

ok but i am sure this is correct. we have the 12.4 for sure. now let us find angle C $\frac{sin(C)}{c}=\frac{sin(B)}{b}$ $sin(C) = \frac{sin(B)}{b}$ $sin(C) = \frac{14 sin(38)}{12.4}$ $C=sin^{-1}(\frac{14 sin(38)}{12.4})$

47. anonymous

my calc gives 44.03

48. anonymous

but don't forget that we rounded b = 12.4. maybe if we don't round we get a more exact answer.

49. 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.

50. anonymous

ok so A =43.9

51. anonymous

no that was C A you find by subracting: 180 - 38 - 43.9=98.1

52. anonymous

wanna try the next one?

53. anonymous

sryy gotta go thanks for the help tho

54. anonymous

welcome