trigonometry

[sacred wagon]

find the missing side and round to the nearest tenth

[sudden python]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[sacred wagon]

degree: 52
side (that is shown): 15

[warm shell]

so we know that cos(x) is hyp/adj

so in this case we know what x is

x is 52

and hyp is 15

so we havw

[sacred wagon]

wait 52 is the degree

[warm shell]

yes

52 is what we plug into the cosine

to get that

so we have this

$\cos(52) = \frac{x}{15}$

wait wrong

lol

[sacred wagon]

oh lmao

[hushed beacon]

Best Trial Mod #Seven

[warm shell]

SOH-CAH-TOA

so because of this

we can just solve for x

so what does x equal?

[sacred wagon]

wait is it always cos (x)

[warm shell]

no no

solving for x in the equation I just sent

try that

[sacred wagon]

oh

so x=15 (times) cos(52)

[warm shell]

yep

so you round the the nearest thenth so

tenth*

,calc cos(52)*15

[hushed beacon]

Result:

-2.4448617119356

[warm shell]

okay so that is weird

lmao

ohh

[sacred wagon]

lmfao

[warm shell]

lmao

that is in radians

,w cos(52)*15 in degrees

[hushed beacon]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by sevenxavior

[warm shell]

something is wrong lmao

[sacred wagon]

wait so is the answer 9.23

[warm shell]

lemme just use desmos

[sacred wagon]

lol

[odd ruin]

Law of CoSines
[ c^2 = a^2 + b^2 - 2ab \cdot \cos(\gamma) ]

In this case, let's denote the given sides and the angle:

• ( a = 15 ) (one side of the triangle)
• ( b = 18 ) (the other side of the triangle)
• ( \gamma = 52^\circ ) (the angle between the sides ( a ) and ( b ))

The missing side ( x ) is opposite the angle ( \gamma ). Let's use the Law of Cosines to find ( x ):

[ x^2 = 15^2 + 18^2 - 2 \cdot 15 \cdot 18 \cdot \cos(52^\circ) ]

Now, calculate term:

1. ( 15^2 = 225 )
2. ( 18^2 = 324 )
3. ( 2 \cdot 15 \cdot 18 = 540 )
4. ( \cos(52^\circ) \approx 0.6157 )

[warm shell]

9.23492212988

[hushed beacon]

Arithmael FG

[sacred wagon]

oh yay im right

ok tysm

[odd ruin]

👏

[warm shell]

LMAO

yes yes

bro through in gamma for 0 reason

[sacred wagon]

LMFAO

wait so is it always cos (x)

[odd ruin]

No

[sacred wagon]

wait so how do you know if its diff

[warm shell]

okay so here is a general way to explain it @sacred wagon

[sacred wagon]

k

[odd ruin]

Well, the cosine value depends on the angle x. For different angles, the value of cos(x) will be different.

[warm shell]

if you are given the same problem but thing of the angle being A and the hyp being H and the other side being X

for this

we have cos(A) = X/H

so just solve for X

an even more general way

is to notice what trig function is involved here

[sacred wagon]

oh yea ik that but im jst asking if its always cos and not sin or tan

[warm shell]

nah

so take a look at the trig function needed out of the info you have

if you notice we know Hyp and want Adj

so Hyp and Adj is cosine

if it was Hyp and Opp it would be sine

if it was Opp and Adj it would be tan

[odd ruin]

SOH CAH TOA or smhtn

[warm shell]

yeah

[sacred wagon]

oh ok

i think i get it

but im jst gonna pratice here with one more question

[warm shell]

go for it

[warm shell]

bro doesn't know SOH CAH TOA but does know gamma

lol

[sacred wagon]

LMAOO

so here x is hyp right??

[odd ruin]

I remember the mnemonic maan

[warm shell]

yep

[odd ruin]

Anyways good work 👍

Good to see people helping others

[warm shell]

so what parts of a triangle does this involve?

[sacred wagon]

opp and hyp

?

[warm shell]

exactly

so what trig function uses that

[sacred wagon]

sin

[warm shell]

good so what is the equation we can make

[sacred wagon]

sin (38) = x/17?

[warm shell]

almost

remember

SOH CAH TOA

O over H

so it is 17/x

so solve for x in the equation

[sacred wagon]

OHH

ok

[warm shell]

$\sin(38) = \frac{17}{x}$

[sacred wagon]

so now x = 17/sin(38)?

[hushed beacon]

Best Trial Mod #Seven

[warm shell]

exactly

[sacred wagon]

ok

thanks

[warm shell]

no problem

[sacred wagon]

27.61257717??

[warm shell]

27.6125771732

[sacred wagon]

mk

[warm shell]

yeah I just typed it into desmos lol

[sacred wagon]

lmao

i think i gegt it now

tysmmm

[warm shell]

alrighty!

if you need any help ping me

[sacred wagon]

got it

thanks again 🙂