Question

Help

Answer 1

@zarkam21 are you familiar with Law of Cosines?

Answer 2

yes ive problems with voca before so am a little familiar

Answer 3

Okay, if that's the case, what is the Law of Cosines formula? Would you mind typing it here using \(\LaTeX\)?

Answer 4

\[a^2=b^2+c^2-2bc cosA\]

Answer 5

\[b^2=a^2+c^2-2ac cosB\]

Answer 6

\[c^2=a^2+b^2-2ac cosC\]

Answer 7

@Hero

Answer 8

Okay, since you know the formula already, the next step is to assign variables to the given values. Would you mind attempting to do this please?

Answer 9

I attempted to put the equation together

Answer 10

c^2=½^2+6^2-2*½*6(cos*95)

Answer 11

@zarkam21, btw, what are the given values of a and b for the 1st triangle?

Answer 12

I apologize , i dont know where I got 6 from

Answer 13

The corrected equation is :

c^2=½^2+(1/3)^2-2*½*1/3(cos*95)

Answer 14

you there?

Answer 15

@Hero

Answer 16

Am i right?

Answer 17

Yes, that looks good.

Answer 18

Sorry, I was AFK for a bit

Answer 19

so to write that as an answer it would be
x=2pi(n)(cos^-1)
x=cos^-1

Answer 20

Wait, what? You're solving for the missing sides of the triangle. Law of Cosines helps you find the missing side opposite the side of the given angle.

Answer 21

So your final answer should be an approximate value for that side length.

Answer 22

From there, you can just use law of sines to find the rest of the missing angles.

Answer 23

wait so c^2=13/36 right

Answer 24

Where are you getting that from?

Answer 25

Look

Answer 26

What does that have to do with finding the missing sides of the triangle?

Answer 27

isn't c^2 the missing length

Answer 28

Yes, but you need to isolate c in order to find the missing length. Also, there needs to be a value inserted for x if you're going to use software to solve for the missing value.

Answer 29

does it matter what value I put in. im sorry im asking so many questions im just a bit confused

Answer 30

\(c = \sqrt{a^2 + b^2 - 2ab\cos(C)}\)

Answer 31

That is the Law of Cosines formula after isolating \(c\). When using a formula to find a value, isolating the variable to be found is generally the first thing to do.

Answer 32

okay got it so it would be : \[c^2=\sqrt{\frac{ 1 }{ 2 }^2+\frac{ 1 }{ 3 }^2-2*\frac{ 1 }{2 }*\frac{ 1 }{ 3 }(\cos*95)}\]

Answer 33

Actually, it should be:
\(c=\sqrt{\left(\dfrac{ 1 }{ 2 }\right)^2+\left(\dfrac{ 1 }{ 3 }\right)^2-(2)\left(\dfrac{ 1 }{2 }\right)\left(\dfrac{ 1 }{ 3 }\right)(\cos(95^{\circ}))}\)

Answer 34

You get \(c\) by taking the square root on both sides of \(c^2 = a^2 + b^2 - 2(a)(b)\cos(C)\)

Answer 35

c=0.62

Answer 36

So \(c \approx \dfrac{3}{5}\)

Answer 37

You should use the approx symbol when finding values that are not exact.

Answer 38

And the value you present should resemble those you were given to begin with. So if you're given fractional values to begin with, then your result should also be fractional.

Answer 39

If you were given whole numbers, then you would present the answer to the closest whole number unless specified otherwise.

Answer 40

got it

Answer 41

for the second one, im a little confused i dont know what im solving for

Answer 42

like if its cos a , cos b , or cos c

Answer 43

Are you sure you finished with the 1st triangle? What did the instructions say?

Answer 44

solve for the remaining sides and angles

Answer 45

Oh I still have to solve for the angles right?

Answer 46

Exactly

Answer 47

well a triangle adds up to 180degrees

Answer 48

Yup, sure does.

Answer 49

180-95=85

Answer 50

but there are 3 sides so

one side is 95 degrees

85/2=42.5

second and third sides = 42.5 degrees

95+42.5+42.5=180 degrees

Answer 51

You have two missing angles, so using the law of sines formula would take precedence over using "three angles sum to 180" formula

Answer 52

i dont think i am familiar with that. i forgot

Answer 53

?

Answer 54

Law of Sines?
\(\dfrac{\sin(A)}{a} = \dfrac{\sin(B)}{b} = \dfrac{\sin(C)}{c}\)

Answer 55

Note: You only need to use two equivalent fractions simultaneously, not three when calculating a value.

Answer 56

so maybe 95 because that is given

Answer 57

Yes, use the originally given values plus an unknown value to find it.

Answer 58

\[\frac{ \sin(95) }{ 95 }=\frac{ \sin(95) }{ 95 }=\frac{ \sin(95) }{ 95 }\]

Answer 59

so you got c (the missing side) as 3/5 right?

we can angle C, side c, angle A (the unknown), and side A (1/2)

to get

sin(95)/ (3/5) = sin(x) / (1/2) to find angle A

Answer 60

2pi(n)

Answer 61

that's a little weird, try checking your calculator input again

Answer 62

try isolating sin(x) algebraically, then take the arcsin of the result

Answer 63

sin(95)/ (3/5) = sin(x) / (1/2)

solve for sin(x) algebraically then take the arcsin of the result

Answer 64

@Zarkam21, where's your TI calculator for this?

Answer 65

I actually left it at school

Answer 66

which is why im using software

Answer 67

ugh im doing it on paper and i keep getting weird values i got 23.9

Answer 68

sin(95)/ (3/5) = sin(x) / (1/2)

if you notice on the right hand side of the equation, sin(x) is being divided by (1/2) so we just need to multiply by (1/2) to isolate sin(x)

(1/2)sin(95)/(3/5) = sin(x)

then taking the arcsin of this gives us

x = arcsin[(1/2)sin(95)/(3/5)]

hopefully wolframalpha likes this input a little better

Answer 69

try without the x = part

Answer 70

just try this as the input

arcsin[(1/2)sin(95)/(3/5)]

Answer 71

56.12

Answer 72

good, so we have angle A (56.12 degrees), angle B (unknown) and angle C (95 degrees), then simply subtract 180 - angle A - angle C to find angle B

Answer 73

180-56.12-95=28.88

Answer 74

so that is the missing angle

Answer 75

good, so that's the triangle solved

would be a good idea to close this and re-open a new question since it's getting pretty long

Answer 76

we are done though with the first one

Answer 77

i will be back in about a hour then we can continue if you are still on

Answer 78

is that alright

Answer 79

sure