Question

Solve remaining angle, please help!

Answer 1

Which angle is it?

Answer 2

A B and C

Answer 3

Well for this you will have to use the law of sines and cosines because its not a right triangle

Answer 4

@douglaswinslowcooper

Answer 5

law of cosines

c^2 = a^2 + b^2- 2 a b cos C

where a and b are on each side of angle C and c is opposite it.

law of sines

a/sinA = b/sinB=c/sinC

Answer 6

I have not done it, so I cannot show you in detail, and I am leaving soon. Maybe another OSer will.

Answer 7

@douglaswinslowcooper gave you the formula you need...
\[c^{2}=a^{2}+b^{2}-2ab(\cos C)\]
where a, b, and c are the sides of the triangle.

find the angle C first, and then use the law of sines like before...

Answer 8

yes I know the formula but I don;t know exactly how to find C. And I'm not sure which sides are which @mtbender74

Answer 9

actually...they gave you the angle names...the side opposite the angle shares its name...side c is opposite angle C, and so on

Answer 10

a=270, b=442.85, c=255

Answer 11

is C is 255, A is 270 and B is 442.85

Answer 12

oh ok I see. so what is the formula for finding C?

Answer 13

sides are lowercase...angles are uppercase

Answer 14

the law of cosines above.

Answer 15

right but that uses Cos C which I don;t know

Answer 16

that's what you solve for...get cos C by itself and then that the inverse cosine

Answer 17

that will tell you the angle C.

once you get one angle, use the law of sines to get another...then subtract from 180 (if using degrees) or pi (if using radians)

Answer 18

How do I get C by itself? Do i say arcsin C= c^2…..

Answer 19

once you plug in the values for the sides and do some simplification, you'll have cos C = some number.. let's say x

C = cos^(-1) x

where cos^(-1) is the inverse cosine function

Answer 20

\[\cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}\]

calculate the piece on the right and then plug it into your cacluator and hit the cos^(-1) button

Answer 21

i'm going to be leaving very soon...i hate to do that to people, but i've got to get going...do you have a start on an answer?

Answer 22

sort of hold on

Answer 23

I know the equation but I can't seem to calculate it. cos c= 270^2 + 442.85^2 - 255^2 / 2(270)(442.85). what did you get

Answer 24

that looks good...plug all of that into the calculator and what do you get? on the right side...

Answer 25

its not letting me calculate for some reason

Answer 26

1.48?

Answer 27

no...calculate the squares and then use just those numbers (add and subtract and divide) as separate steps...

Answer 28

i have to go...sorry... :(

Answer 29

I tried that my calculator isn't working. Could you tell me what you got?

Answer 30

I already know the equation

Answer 31

i get 1.396 on the right...take the inverse cosine of that....and that is C

Answer 32

Im just getting undefined

Answer 33

try it using the calculator in windows....set the view to scientific...

Answer 34

cos^-1 (1.396) = undefined

Answer 35

sorry...not good at trig and inverse functions

Answer 36

ok

Answer 37

yes, arc cos(1.36) is undefined because there is no angle that gives a cos value larger than 1
re-do your calculations

Answer 38

@washcaps
The error in your calculation is that you ADDED all three terms a^2+b^2+c^

It SHOULD be a^2+b^2-c^2

The 3rd term is subtracted.

Answer 39

@douglaswinslowcooper I get 1.21955

Answer 40

@mrnood

Answer 41

@mathmale can you help? I know the formula but can't solve

Answer 42

When I do the first portion of the formula I get 1.48

Answer 43

Another student got to me first; I'll be with you as soon as I can.

Answer 44

Right so arccos B= 270^2+255^2-442.85^2 - 2(270)(255)

Answer 45

Please take another look at the Law of Cosines that I typed out for you just a minute back. To solve for cos B, you're going to have to do some division. I don't see any division in your tentative answer.

Answer 46

sorry I meant arccos B= 270^2+255^2-442.85^2 / 2(270)(255)

Answer 47

While I'm not checking every detail, that expression looks correct. Would you mind evaluating it? Since "degrees" are probably more familiar to you than are "radians," set your calculator to "degree" mode, if you haven't already done so.

Answer 48

If your calculator is a TI-83 or -84, type in the following:
\[2nd~\cos~(your~value~of~\cos~B)~ENTER\]

Answer 49

1.48 radians so 84.8 degrees

Answer 50

Again, I'm not doing the actual work, but that result appears to be reasonable.

Answer 51

so do I do cos^-1(1.48)?

Answer 52

You could check it by pretending that you don't know the value of b (the length of a side). Apply the Law of Cosines again:

\[b^2=a^2+c^2-2(a)(b) \cos B\]

Answer 53

where B is the angle that you've just found. If b turns out to be 442.85 or so, you'll know you're right.

Answer 54

the problem is that Cos^-1(1.48) doesn't equal anything

Answer 55

@mathmale

Answer 56

270^2+255^2-442.85^2 / 2(270)(255)

=-0.42259

B=arcos(-.42259) =115 deg

Us sine rule for the other angle

Answer 57

@MrNood so 115 degrees is the answer for B? how do I go onto finding C and A? I know use the sine rule, but how exactly do I set it up

Answer 58

Once you have B, using the Law of Sines might be faster than using the Law of Cosines to find the remaining 2 angles.

Answer 59

C=31.4575? I got this by doing C=sin^-1=255sin(115degrees) / 442.85

Answer 60

I'm afraid not. Review the Law of Cosines and ensure that you've included EVERYTHING in that formula.
Or, use the Law of Sines...you'll need to know this later anyway.
Unfortunately, I need to get off the 'Net now. Might be back later.

Answer 61

Once you have the angle B (I gave it to you above) you do not need the cosine rule

Use the sine rule - you say you know it, so use it to find one of the other angles

After that use the sum of angles = 180 to solve the third

It is just 1 step you need to make for yourself -use the sine rule