Use the triangle at the right. Find the length of the missing side.
Show your work
Did i do the first one right? I don't want to do the second one wrong too.
1.a = 16, b = 63 2. b = 2.1, c = 2.9
16^2 =256, 63^2=3,969
256+3969 = 4225 now we need to find the square root by separating the 4225 into two separate numbers square root of 42 is 6 now find the largest root in 42. Which is 36.
6*6 = 36 and the square of 25 is 5 add the roots
This give me the answer for c length. 6 and 5 is 65.
a=256 b=3969 and c = 65

- anonymous

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- SolomonZelman

Do you have a picture or other description of the triangle you are dealing with in problem 1 and/or problem 2?

- anonymous

yup you need a picture

- anonymous

The picture probably wouldn't help it's just a right triangle but okay

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- anonymous

@SolomonZelman

- SolomonZelman

this picture will definitely help, because I would have thought that b is the hypotenuse

- SolomonZelman

i mean in question 1 i would have thought so, but this picture gives me that c=hypotenuse in both cases, and I know it is a right triangle

- anonymous

Alright.

- SolomonZelman

I want to correct you though.
The set up is a little different, that is 1.
Here is the rule.
A right triangle with sides a, b, c (where the hypotenuse is side c), must
satisfy the following statement:
a²+b²=c²

- SolomonZelman

this statement is known as the pythagorean theorem.

- SolomonZelman

Now, you are given your two smaller legs a and b are 16 and 63 (respectively).
And you are missing the hypotenuse, so this is what you would do.
(16)² + (63)² = c²

- SolomonZelman

then you simplify the left hand side, and solve for c (just by talking the square root of both sides)

- anonymous

So i had to square c?

- anonymous

Take the square root of a and b?

- SolomonZelman

(16)² + (63)² = c²
4225 = c²
then do this:
\(\sqrt{4225}\) = \(\sqrt{{\rm c}^2}\)

- SolomonZelman

this way you are able to solve for c.
(normally the square root will give you the ±, as you know, but in this case since distance or sidelength can not be negative, you diregard any negative solutions)

- anonymous

Alright. is c 65? @SolomonZelman

- SolomonZelman

yes

- anonymous

Did i do the problem right?

- SolomonZelman

i wrote it all out and still doesn't take that much space and time.....
ok, now question 2...

- anonymous

Kay.

- SolomonZelman

oh, I deleted that....
------------------
a²+b²=c²
16²+63²=c²
4225=c²
√4225 = √c²
c=65
------------
reposted it.

- SolomonZelman

ok, in question 2, you are given
c=2.9
b=2.1

- SolomonZelman

can you plug in this information into the a²+b²=c² ?

- anonymous

Sure a^2+ b^2=c^2

- SolomonZelman

but, you are given the c and b, so you can g ahead and plug in 2.9 for c, and 2.1 for b.

- anonymous

2.9^2 + 2.1^2

- SolomonZelman

no,

- SolomonZelman

The pythagorean theorem is:
a²+b²=c²
where c is the hypotenuse and a & b are two legs.
you are given that your c (which is hypotenuse as well) is 2.9
and you are given that your b is 2.1
(your missing side is a)

- anonymous

Alright

- SolomonZelman

please take a shot to plug in your values (into a²+b²=c²)

- anonymous

2.9^+2.1=c^2

- SolomonZelman

your c is given, but a is not

- SolomonZelman

it is like this:
a² + (2.1)² = (2.9)²

- anonymous

Oh sorry.

- SolomonZelman

it's ok...

- anonymous

2.9^+2.1=c^2

- SolomonZelman

a² + (2.1)² = (2.9)²

- anonymous

Wifi is bad okay a^2 +(2.1)^2 =( 2.9)^2

- SolomonZelman

because you are given:
c=2.9
b=2.1
so, the missing side is a.
Our theorem is:
a² + b² = c²
so lets plug in everything
plugging 2.9 for c
plugging 2.1 for b
you get:
a² + (2.1)² = (2.9)²

- SolomonZelman

ok now solve for a

- anonymous

Alright one moment

- anonymous

Do i add the c value or divide or do it the same thing i did in my last problem.

- anonymous

@SolomonZelman you there?

- SolomonZelman

you first calculate the values of (2.1)² and (2.9)²

- anonymous

Alright.

- anonymous

4.41= 8.41. Do i subtract next?

- SolomonZelman

a² + (2.1)² = (2.9)²
without a calculator:
21•20=420
21•21=420+21=441
so 2.1² = 4.41
30•30=900
30•29=900-30=870
29•29=870-29=841
so 2.9²=8.41

- SolomonZelman

just demonstrating another technique.

- SolomonZelman

anyway
a² + (2.1)² = (2.9)²
a² + 4.41 = 8.41
yes you subtract 4.41 from both sides

- anonymous

Okay.

- SolomonZelman

a² + 4.41 \(\small \color{red}{-4.41}\)= 8.41\(\small \color{red}{-4.41}\)

- SolomonZelman

and from this u get?

- anonymous

4.00

- SolomonZelman

yes, or just 4 :)

- SolomonZelman

so, a²=4
correct?

- anonymous

Yeah it looks correct i don't think it can be factored anymore

- SolomonZelman

no, there is no factoring here:)
so we got
a²=4
what do you think your next (and final) step is?

- anonymous

putting them together like 2.1^2+2.9^2= 4^2

- SolomonZelman

u just take the square root of both sides
\(a^2=4\)
\(\color{red}{\sqrt{\color{black}{a^2}}}=\color{red}{\sqrt{\color{black}{4} }}\)

- SolomonZelman

a = ?

- anonymous

4^2?

- SolomonZelman

a square root of a 4 is?

- anonymous

2?

- SolomonZelman

yes
so a=2

- anonymous

Alright is there anything else?

- SolomonZelman

no, you found the missing side in both of the problems.

- anonymous

Alright thanks for your help :)

- SolomonZelman

yw

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