Question

What is the area of the triangle below?

Answer 1

@sleepyjess When you get back

Answer 2

Is there a given right angle or is that it?

Answer 3

Nope, that's it...

Answer 4

Okay, have you learned about Law of Sines, Law of Cosines and Heron's Area Formula?

Answer 5

No, I haven't

Answer 6

I would assume since you haven't that there is a 90 degree angle involved

Answer 7

I was supposed to learn about it but I have been absent

Answer 8

oooohhh so you are supposed to know Law of Sines, Cosines and Heron's?

Answer 9

Yes, I can google it. I don't expect you to teach me that lol ;P

Answer 10

I just got done learning about it haha

Answer 11

They are all just a bunch of formulas to remember, not TOO hard.

Answer 12

^ exactly

Answer 13

In this problem you just need one law of cosine. Then the heron's formula.

Answer 14

again, not the best at drawing

Answer 15

So law of cosines for finding side a
\(a^2 = b^2 + c^2 - 2(b)(c)(cos A)\)
pretty simple actually :)

Answer 16

Gonna let @sleepyjess explain all that.

But seriously, copy down these formulas. No way your gonna remember them in your head (at least for now)

Answer 17

Those formulas are a bit complex...It's amazing that someone actually discovered all these relations and equations....

Answer 18

That's what I thought haha

Answer 19

My lessons actually gave the formulas already changed up to find a missing angle if you want me to put them here

Answer 20

Okay :)

Answer 21

But for this problem, we just need a missing side :)

Answer 22

\(cos A = \dfrac{b^2 + c^2 - a^2}{2bc}\)

\(cos B = \dfrac{a^2 + c^2 - b^2}{2ac}\)

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

I saw these and was like, how am I supposed to use these?????? But once you plug in everything, it actually is quite simple :)

Answer 23

Okay, so I need to find the cosine of every angle?

Answer 24

No haha
I was just giving you those for future reference
we just need to find side a

Answer 25

So what would the first step be?

Answer 26

Using one of the formulas tan put up, \(a^2 = b^2 + c^2 - 2(b)(c)(cos A)\)

Answer 27

Okay so
a(sq) = (3*3) + (7*7) - 2(3)(7)(cosA)
a(sq) = 58 - 42(cos(55))
a(sq) = 58 - 24.1
a(sq) = 34
a = 5.8

Answer 28

I'll give dtan a medal, too because you both helped me :)

Answer 29

Your work above is correct to!

Answer 30

Yay! :)

Answer 31

Awwww yeauhhhhh ! \m/ xD

Answer 32

Now you have one remaining step, using the heron's formula. Go give it a try.

Answer 33

Whoops, I totally forgot that we were finding the area haha
I think tan can finish you off from here :)

Answer 34

Haha, thanks.

-Start by adding up all the sides and dividing by 2, to get your value of S in the formula.

Answer 35

So wouldn't that just be S = 180/2?
Because the sum of the angles in a triangle = 180 degrees

Answer 36

If the above is true then 8.7 = 90 ? wut

Answer 37

there is a solid difference between angles and sides lol

Answer 38

OH!! A B and C are referring to the sides.......
Wow I am so tired lol ;P

Answer 39

wowwwwwww

Answer 40

you know, it's funny that you we actually could have used a law of sin to get the area directly and not do all this cosine/heron formula but.....bit late now LOL

Answer 41

SORRY LOL

Answer 42

but it's good to know both ways anyhow

Answer 43

so continue with the heron formula.

Answer 44

Haha, nice. Well I like math so it's alright 8)
Anyways here's the work :
S = A+B+C/2
8.7 = A/2 + 5 ?

Answer 45

Wow. sorry for the complete lack of intelligence here. I am barely awake

Answer 46

i'm not sure what you did..

but you simply add up the sides here

5.8+3+7

divide that sum by 2

Answer 47

Here we go for real :
8.7 = A+B+C/2
8.7 = 5.8+7+3/2
8.7 = 15.8/2
8.7 = 7.9
what is going on here lol -_-

Answer 48

where are you getting the 8.7 from?

Answer 49

s=7.9, that is all.

Answer 50

-facepalm-

Answer 51

now i suggest a calculator and just plug everything in to that heron formula..and your done.

Answer 52

Yessir

Answer 53

don't worry my eyes are just as redshot as yours. xD

Answer 54

What do you mean by that? ^ lol

Answer 55

redshot=so tired your eyes are straining to keep open, hence the fact that they are red.

Answer 56

Yep.

Answer 57

can we also not just drop a perpendicular in there to find the height? Considering \[A=\frac{1}{2}bh\]