Question

I need help on math. I'll attach a ss below.

Answer 1

@jhonyy9

Answer 2

@az

Answer 3

@snowflake0531

Answer 4

You first have to use the pythagorean theorem to find the third side of the triangle

can you do that

Answer 5

Kind of

Answer 6

\[2\sqrt{21}^{2}=x ^{2}+3\sqrt{2}\]

is that it?

Answer 7

\[3\sqrt{2}^{2}\]
that's what the last one supposed to look like

Answer 8

almost, but let's add parenthesis so we don't get confused that it's the square of the whole number

\( (2 \sqrt{21})^2 = x^2 + ( 3\sqrt{2})^2\)

Answer 9

now let's solve for x but first let's find out what those numbers are when you \(^2\) to them

so you should know that
\( (ab)^2 = a^2 b^2\)

and that \(\sqrt{x} ^2 = x\)

Answer 10

so we have

\( (2 \sqrt{21})^2 \)

what do you get when you square it?

Answer 11

would that be that side?

Answer 12

Yes!

Answer 13

Now do you know that

tan = opposite / adjacent

Answer 14

so √66 / 3√2?

Answer 15

Yup!

Answer 16

I'm not sure if that is an acceptable answer or if they want us to multiply by \(\sqrt{2}\) in the numerator and denominator so that way we don't have any square root in the denominator

Answer 17

?

Answer 18

Well, you are on a roll!

Answer 19

So let's simplify it a little more

132 = 33 * 4

so what is \(\sqrt{132} =?\)

Answer 20

I don't think that will work bc I get a decimal I think I need something like

number√number

is that makes sense

Answer 21

\[2\]\[2\sqrt{33}\]

Answer 22

yes, I understand but remember you can pull out the 4

yes!

Answer 23

So now you have

\( \dfrac{2\sqrt{33}}{6}\)

you can simplify it just a little bit more and get rid of that 2
what does the denominator become?

Answer 24

would the answer be
\[\sqrt{33} / 3\]

Answer 25

That would be your final answer!

Answer 26

Thank you so much!!!! Do you think you can help me on one more?

Answer 27

wait

Answer 28

okay

Answer 29

okay, yup that was the correct answer! And sure :)

Answer 30

cosine is opposite / hypotenuse right?

Answer 31

No, that's sin

SOH CAH TOA

Sin = Opposite / Hypotenuse

Cos = Adjacent / Hypotenuse

Tan = Opposite / Adjacent

Answer 32

so now I have to find the adjacent side?

Answer 33

yeah, they really are making you do a lot of work for these questions hmm

Answer 34

Use the Pythagorean theorem to find the adjacent side and then we use the ratio adjacent / hypotenuse and simplify it

Answer 35

x=√74

Answer 36

are you saying that's the adjacent side?

because I got a different answer for that mhmm

Answer 37

oh well I thought it was the adjacent side

Answer 38

it would be √148?

Answer 39

so if we use the Pythagorean theorem

\( x^2 = (2\sqrt{74})^2 - (2\sqrt{37})^2\)

Answer 40

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jkmiec26
it would be √148?
\(\color{#0cbb34}{\text{End of Quote}}\)

Yes!

Answer 41

@AZ ??

Answer 42

ah, okay, let's take a step back

148 = 74 * 2

so

\(\sqrt{148} = \sqrt{2 \times 74} = \sqrt{2} \times \sqrt{74}\)

so now you can just cross out sqrt(74) from both the numerator and denominator

Answer 43

would the answer be
\[5\sqrt{437} / 148\]
??

Answer 44

no, you cannot simplify sqrt(10952) to 5 sqrt(437)

I don't know how you did that

Answer 45

But let's go back one step before you multiplied it all

Answer 46

remember

\(\sqrt{a\times b} = \sqrt{a} \times \sqrt{b}\)

so
\(\sqrt{148} = \sqrt{2 \times 74} = \sqrt{2} \times \sqrt{74}\)

Answer 47

sice you get 74 in both can you cancel out?

Answer 48

since

Answer 49

Yes! And what are you left with?

Answer 50

√2 / 2

Answer 51

Tysm! I really appreciate your help

Answer 52

You got it! Well done :))

Answer 53

It was my pleasure!!