Question

Find the m angle T
answers:
40.5°
38.5°
139.5°
124.5°

Answer 1

your using the law of cosine right?

Answer 2

you are correct

Answer 3

so what do you get when you do?

Answer 4

gotta work it out

Answer 5

alright

Answer 6

I don't know how I would put it

Answer 7

t^2 = s^2 + r ^2 ?

Answer 8

the law of cosines is

c^2 = a^2 + b^2 - 2*a*b*cos(C)

so in this case, we would say

t^2 = r^2 + s^2 - 2*r*s*cos(T)

Answer 9

then plug everything in to get

t^2 = r^2 + s^2 - 2*r*s*cos(T)

16^2 = 24^2 + 22^2 - 2*24*22*cos(T)

from here, you solve for T

Answer 10

okay

Answer 11

so I don't do anything with the cos (T) ?

Answer 12

think of it as its own variable

you solve for cos(T) first, then you further solve for T once you have isolated it

Answer 13

so if you really want to, you can replace cos(T) with x

that would mean

16^2 = 24^2 + 22^2 - 2*24*22*cos(T)

turns into

16^2 = 24^2 + 22^2 - 2*24*22*x

Answer 14

then you would solve 16^2 = 24^2 + 22^2 - 2*24*22*x for x like normal

after you have isolated x, you replace x with cos(T)

finally, you would solve for T using the arccosine function

Answer 15

this is what I have so far 256 = 576 + 484 - 1056

Answer 16

so it would be 256 = 576 + 484 - 1056*cos(T)

or 256 = 576 + 484 - 1056x

if you let x = cos(T)

Answer 17

okay then add 576 + 484 ?

Answer 18

yep

Answer 19

then do I subtract from 256 ?

Answer 20

correct

Answer 21

from the 1060 ?

Answer 22

or the 1056 x ?

Answer 23

256 = 576 + 484 - 1056*cos(T)

256 = 1060 - 1056*cos(T)

256 - 1060 = -1056*cos(T)

-804 = -1056*cos(T)

Answer 24

on line 3, we are subtracting 1060 from both sides because you can't combine it with the 1056*cos(T) term

Answer 25

oh right okay okay

Answer 26

then ill divide it

Answer 27

both sides by what

Answer 28

-804?

Answer 29

what do you get when you do that

Answer 30

.7613

Answer 31

so you now have

0.7613 = cos(T)

Answer 32

or

cos(T) = 0.7613

Answer 33

ohh then solve for the rest of it ?

Answer 34

yep, so you use the arccosine to undo the cosine

Answer 35

arccosine and cosine are like division and multiplication

Answer 36

ohh okay I guess hah so I don't solve it like I did in the beginning?

Answer 37

I'm not sure what you mean exactly

Answer 38

like would I still solve it t^2 = r^2 + s^2 since I have to find the angle of T

Answer 39

oh no that only applies if you wanted to find the side lengths (not angles) and if this was a right triangle

Answer 40

oh okay! so then how would I solve this one?

Answer 41

cos(T) = 0.7613

arccos( cos(T) ) = arccos(0.7613) ... apply the arccos function to both sides

T = arccos(0.7613)

T = ??

Answer 42

803.9328 ?

Answer 43

way too high

Answer 44

do you have a TI calculator?

Answer 45

yeah I do the scientific one right?

Answer 46

how are you getting 803

are you hitting "2nd" then "cos" to get arccos?

Answer 47

no.. I don't know what the arcos is ?

Answer 48

i multiplied 1056

Answer 49

what did you type in to get 803 then?

Answer 50

oh i see

Answer 51

well you can type "arccos(0.7613) in degrees" into google without quotes to get this

https://www.google.com/search?hl=&q=arccos%280.7613%29+in+degrees&sourceid=navclient-ff&rlz=1B3GGLL_enUS420US420&ie=UTF-8

Answer 52

google will act like a calculator and spit the result out

Answer 53

ohhhh okay i got that

Answer 54

btw arccos is often found by hitting the \(\large \cos^{-1}\) key

Answer 55

oh you did? well that's your final answer

that's the measure of angle T

Answer 56

yeah i typed that and i got 40.4?

Answer 57

you got it correct, so why did you multiply it by 1056?

Answer 58

i don't know i thought i had to but i guess not lol

Answer 59

nope, once you isolate T, you get

T = 40.4210626 degrees

roughly

Answer 60

so then it would be 40.5 ?

Answer 61

it's actually closer to 40.415439021453

so I would go with 40.4 if you're rounding to one decimal places

Answer 62

place*

Answer 63

aha ohh but it doesn't give me the choice of that so i figure it would be 40.5

Answer 64

odd, well there is a bit of roundoff error I guess

Answer 65

40.5 works if they're using approximations

Answer 66

i think so. but thank you so much! :)

Answer 67

sure thing