Question

Help would be really appreciated! Find all the missing parts to the triangle below...

Answer 1

http://www.aventalearning.com/courses/GEOMx-HS-A09/b/assessments/R-LawofCosinesShortAnswerQuiz/Geometry_8.4.14_Quiz_FINAL_10q.gif

Answer 2

Do yhu know the SAS formula?

Answer 3

Yes, but the problem is related to the Law of Cosines.

Answer 4

@ranga

Answer 5

Ok. c:

Answer 6

Yhur formula is Area= 1/2 ab sin (C)

Answer 7

Are you sure..?

Answer 8

she doen't need area?

Answer 9

Yes, Do yhu know how to work that out?

Answer 10

No, Yhu have to find the missing parts of the triangle, the missing measurements.

Answer 11

I only need the missing leg and angles.

Answer 12

Using that formula, yhu'll get yhur missing leg.

Answer 13

Oh wait... Hang on.

Answer 14

law of cosines
\[c^2 = a^2 + b^2 - 2ab \cos C\]
law of sines
\[\frac{\sin A}{a} = \frac{\sin C}{c}\]

Answer 15

Beat me to it. :D

Answer 16

a = 15
b = 28
C = 87

Answer 17

c^2=15^2+28^2-2(15)(28)cos87

Answer 18

Right?

Answer 19

Yes.

Answer 20

I got 965.03

Answer 21

√965.03=31.06 , correct?

Answer 22

I got 225+784-840= 169 times cos87= 8.84

Answer 23

@mathmale

Answer 24

@tgawade assistance is required.

Answer 25

@Cubi-Cal , you are correct

c = 31.065

Answer 26

D. C. provided the correct formula. D. C.: Please discuss with Cubi-Cal how you arrived at this final result, so that all the steps of the process are clear. Thanks.

Answer 27

Okay great! So that would take care of which part of the triangle?

Answer 28

the 3rd leg...part "f"

Answer 29

Ah okay.

Answer 30

So how do I use f to solve the angles, now?

Answer 31

since (GH)^2 = 980.73 so GH = 31.316

Answer 32

Use laws of sine

Answer 33

Law of sines

\[\frac{\sin H}{15} = \frac{\sin 87}{31.065}\]

Answer 34

SinH31.065=14.97

Answer 35

Correct?

Answer 36

yes

Answer 37

Okay, then would I do arcsin14.97? Which gave me .99

Answer 38

I'm assuming that this is the problem you wanted to discuss. Is it? If so, let's summarize what we already know: 2 sides are 15 and 28, and we've found f, the third side. What is it? We have one angle, which is 87 degrees. Correct?

Answer 39

Yes this is the problem! f=31.065

Answer 40

Which of the unknown angles would you like to find first? The known angle is 87 degrees.

Answer 41

We could do G first.

Answer 42

Have you used the Law of Sines before?

Answer 43

Yes!

Answer 44

Great. You want angle G. You have side g = ??

Answer 45

g would be 15, right?

Answer 46

It's side h that is 15. Note that side h is opposite angle H.
You want angle G. the side opposite angle G is g = ??

Answer 47

Think: g is opposite angle G, h is opposite angle H.

Answer 48

28!

Answer 49

To find angle G use laws of sine ... sinG/28 = sin87/f

Answer 50

Right. You want angle G. You already have side g, which is 28, as well as h, which is 15, and f, which is 31.065.

Write out this equation:

sin G sin 87
---- = ----------
g 31.065

Answer 51

This is the Law of Sinces applied to finding angle G. Actually, we find sin G first, then G itself. Want G in degrees or rad?

Answer 52

SinG31.065=.99g

Answer 53

Probably rad.

Answer 54

(Looking at your equation.)
But since angle F is given in degrees (87 degrees), you should look for angle G in degrees also.

Answer 55

Oh right.

Answer 56

Strong suggestion: Use parentheses to make your equation easier to read and understand:

31.065sin G = (g)sin 87

Answer 57

But g is known, isn't it? If so, replace g with its value in your equation, above.

Answer 58

SinG 31.065=27.96

Answer 59

That looks good; I'd been looking for 31.065 sin G = 28 sin 87.

Answer 60

How would you now isolate "sin G"?

Answer 61

By using arcsin?

Answer 62

not yet; have to have sin G alone on the left side first.

After that, then yes, you do need to use the arcsin function.

Answer 63

Um.. division then?

Answer 64

If not subtraction?

Answer 65

I'd prefer you write this equation as 31.065 sin G = 28 sin 87.

Divide both sides by 31.065 now.

No subtraction is involved here.

Answer 66

Okay I got .9001

Answer 67

So did I! Now please find the inverse sine of that.

Answer 68

Okay, great! That would be 64.17

Answer 69

When I round that off, I get 64.17.

Actually, with quantities given in the original problem as 15, 87 and 28, we should be rounding everythign off to the nearest integer.

But for now, say G = 64.2 degrees. Agree with that? You wanted G.

Answer 70

Got it! I agree!

Answer 71

So lastly is H.

Answer 72

Now you have a triangle with two angles known: they are 64 and 87. Hint: What is the sum of the interior angles of a triangle?

How would u use this fact to find H?

Answer 73

OH! 64+87+29=180

Answer 74

Cool.

Answer 75

any questions about using either the Law of Sines or the Law of Cosines?

Answer 76

Yes, would you mind checking my work in a previous question?

Answer 77

Could you possibly give me the URL of that question?

Answer 78

Yes.. http://openstudy.com/study#/updates/4f887586e4b02251ecc96433