Question

In triangle DEF, m angle D= 43º, m angle E=62º, and EF=22 in. What is DE to the nearest tenth of an inch?
a. 28.5 in
b. 15.6 in
c. 14.1 in
d. 31.2 in

Answer 1

set it up like a proportion

Answer 2

proportion?

Answer 3

so D is the angle opposite of EF and F is the angle opposite of DE

so first you have to find F

Answer 4

180-105=75

so that is angle F

to find DE you have to set up a proportion like this
43/22=75/x

cross multiply

Answer 5

22 x 75 =21650

then divide that by 43

Answer 6

1650*

Answer 7

You're a lifesaver, thank you.

Answer 8

you're welcome

Answer 9

I got 38. But that can't be right.

Answer 10

I used the wrong thing I'm sorry. hold on I got it though

Answer 11

It's okay (:

Answer 12

okay I got it

a/sinA=b/sinB=c/sinC

the capital letter is the angle the lower case is the side

Answer 13

sweet. how would i plug that in? i keep forgetting .___.

Answer 14

okay so it would be like this

d/sinD=f/sinF

side DE=what we don't know so that would
side EF=22
angle D=62
angle F=75

do you think you can plug that in

Answer 15

I'll try :3

Answer 16

d/sin(62 = f/sin(75)

Answer 17

f=22

Answer 18

d/sin(62)=22/sin(75)

Answer 19

then just multiply 22 x sin(62)

then divide that by sin(75)

Answer 20

no wait f= is what we don't know so d=22

Answer 21

sorry I'm just kinda tired

Answer 22

22 x sin(75)

divide that by sin(62)

Answer 23

same... i'm behind in math so i'm paying for it ha.
i'll let you sleep. i'm sure i can figure it out, thank you.

Answer 24

okay

Answer 25

im gonna change DEF to ABC respectively just because i find it easier to visualize it that way... so basically you know m of angle A is 43 degrees, the m of angle B is 62 degrees, and the line from E to F (aka d) = 22 in. correct?

Answer 26

in that case you would do another version of cross multiplication using sine. so you would put the sin of 43 or sin43/22 because those two are the A and the little a and make that multiplied with the sin of B or sin62/(x) so then you have the sin43= sin62*22 which is....

Answer 27

some long number that i'm too tired to type out anyways so then you divide that number by the sin of 43 and you get about 28.5 by my calculations

Answer 28

so A is your answer. hope that made sense i'm pretty tired XD

Answer 29

the way i write it is sort of strange basically you have sin62/x=sin43/22. The easier way for me to look at it is as x/sin62=22/sin43 so then you just do 22sin62/sin43=x and simplify

Answer 30

i hope that's a bit clearer

Answer 31

THANK YOU! :D

Answer 32

sure thing :)

Answer 33

i just finished this lesson haha so i remember how to do it XD

Answer 34

any other ones you need help on?

Answer 35

yooo, so you did the unit test? YES I DO OML

Answer 36

Half of them are chinese to me xD

Answer 37

oh boy... haha

Answer 38

wait wait, i might be exaggerating.

Answer 39

*thinks about it* nah...im not exaggerating XD

Answer 40

number 8 (hopefully we have the same question) it says. find the height of the triangle. round the answer to one decimal place.

Answer 41

I swear i thought i had this, then bam i forgot .___.

Answer 42

nope, dont have that. could you send a picture?

Answer 43

pickles. sure hold on.

Answer 44

haha sure thing

Answer 45

Swear I'm not cheating but I'm so lost.

Answer 46

mmk so same thing here. for the sake of understanding me im going to say the measure of angle a is 50 degrees, the measure of angle B is 90 degrees, the measure of angle C (which you dont actually need to know here) is 40 degrees, little a is x and little b is 10. you with me so far?

Answer 47

from there, set it up like we did last time with big letter over little letter for what we know with all degrees being the big letters and all the segments being the little ones

Answer 48

so you have sin50/x=sin90/10

Answer 49

i hate looking at it like that so for me it's easier to see x/sin50=10/sin90 which is for our purposes the same exact thing. so you multiply both sides by sin50 to get 10sin50/sin90=x

Answer 50

wowzers, im writing this down

Answer 51

if my calculator is right then you get about 7.7 and im not going to question my calculator... XD

Answer 52

i hope you can see that XD my handwriting is kinda small

Answer 53

so is mine xD i can see it

Answer 54

mmk so does that make sense?

Answer 55

i could find little c the same way but im lazy and if im not asked to do it for credit then i wont haha

Answer 56

it makes sense, i wont ask you to find the c xD

Answer 57

YAY!! :D

Answer 58

ok so next one?

Answer 59

well actually, why dont you just find the little c and ill do it too and that way you can make sure you get it.

Answer 60

i'll do it after this test, it's 1 am here xD i have a few more questions to finish.
okay next question

Answer 61

haha ok

Answer 62

for number 11, D is 68.8m^2

Answer 63

its 1 here too but...insomnia...so ya doesnt really bother me much anymore XD

Answer 64

your tests are awfully annoying arent they.... XD

Answer 65

Yes!! so very annoying ;-; i have a final coming up next so basically I'm about to die an annoying death.

Answer 66

haha ill join ya.

Answer 67

ok so i would first try to find little a or line segment bc because that makes life easier

Answer 68

so a^2 + b^2 = c^2 so you have 23^2 = 7^2 + a^2

Answer 69

= 529 = 49 + a^2. subtract the 49s and you have 480=a^2 rad of 480 is about 21.9

Answer 70

with me so far?

Answer 71

yeah :D

Answer 72

ok yay. so then you plug in what you know using the big letter over little letter formula (forgot the actual name XD) so you have sin(x)/21.9 = sin90/23

Answer 73

so you have sin(x) = 21.9sin90/23

Answer 74

(quick tip the sine of 90 is 1 so anything in front of a sin(90) is that number so in this case you just have 21.9/23)

Answer 75

which is some long complicated number and im lazy XD ok so from there, you have to do the arc sin of that number or sin^(-1) to find your degree

Answer 76

my calculator says 72.2

Answer 77

but 72.3 also works

Answer 78

make sense?

Answer 79

strangely enough yes

Answer 80

haha yay

Answer 81

so i've been getting them right xD

Answer 82

number 11? i'm not so sure on that one.

Answer 83

mmk

Answer 84

fudge...this uses the longer equation...hold on...

Answer 85

I KNEW IT. Pickles

Answer 86

a^2 = b^2 + c^2 - 2(b)(c)cosA is your equation and you can move those values around if your equation asks it

Answer 87

your problems are not enjoyable at 1 in the morning my friend

Answer 88

here we go

Answer 89

i feel.

Answer 90

wait, it's gotta be C. 48.2

Answer 91

what is option D?

Answer 92

68.8m^2

Answer 93

not so sure about that but interwebs....

Answer 94

in which case A is your closest answer