Question

Find a if b = 60 and c = 61.
Right triangle with sides a, b, and c. Side c is opposite the right angle.
A. a = 121
B. a = 1
C. a = 11
D. a = the square root of7321

Answer 1

We have a right triangle. So we can use the Pythagorean Theorem to solve for 'a'

Answer 2

a^2 + b^2 = c^2

a^2 + 60^2 = 61^2

a^2 + 3600 = 3721

...
...
...

a = ???

Answer 3

So it would be B?

Answer 4

a^2 + 3600 = 3721

a^2 + 3600 -3600 = 3721 - 3600

a^2 = 121

a = ???

Answer 5

A? .-.

Answer 6

that's a^2, not 'a'

Answer 7

what undoes squaring?

Answer 8

Would you subtract?

Answer 9

what operation is the opposite of squaring?

Answer 10

Square root?

Answer 11

good, so take the square root of both sides

Answer 12

It would be C?

Answer 13

yes because \(\Large \sqrt{121} = 11\)

Answer 14

Okay thanks so much. Do you mind helping with several more?

Answer 15

I can do a few more, sure

Answer 16

Okay thanks.

Answer 17

An airplane lands at an airport 60 miles east and 25 miles north of where it took off. How far apart are the two airports?
image of a triangle with a box in the lower right corner; the horizontal side forming that corner is labeled 60 miles and the vertical side forming that corner is labeled 25 miles
A. 65 miles
B. 54.54 miles
C. 13.04 miles
D. 9.22 miles

Answer 18

a^2 + b^2 = c^2

60^2 + 25^2 = x^2

solve for x

Answer 19

So..

120+50=c2 ?

Answer 20

60^2 means 60 squared

NOT 60 times 2

Answer 21

Oh goodness I knew that. My apologies.
So

3600+625=c2

Answer 22

that's ok

Answer 23

now add to get _____

Answer 24

4225?

Answer 25

good

Answer 26

so

\[\Large x^2 = 4225\]

how do we isolate x?

Answer 27

I'm not to sure.

Answer 28

we do the same thing we did back when we solved for x in \(\Large x^2 = 121\)

Answer 29

So it would be 65?

Answer 30

you nailed it

Answer 31

With your help of course. Thank you for taking the time to explain it.

Answer 32

you're welcome

Answer 33

Find c if a = 5 and b = 12.
Right triangle with sides a, b, and c. Side c is opposite the right angle.
A. c = 17
B. c = the square root of17
C. c = 13
D. c = the square root of13

Answer 34

So this would be

25+144=169=13

Answer 35

you are correct, but the notation and the way you wrote it is a bit off

you should have \(\Large \sqrt{169} = 13\) but you have the right idea

Answer 36

Yeah I just didn't know how to put that.

Answer 37

oh you can type sqrt to mean "square root"

so sqrt(169) is the square root of 169

Answer 38

Therefore this would be B?
Find c if a = 3 and b = 5.
Right triangle with sides a, b, and c. Side c is opposite the right angle.
A. c = 4
B. c = the square root of34
C. c = 8
D. c = the square root of15

Answer 39

Thank you.

Answer 40

B) \(c = \sqrt{34}\) is correct

Answer 41

YAAAAY!

Answer 42

sounds like you got the hang of this, that's good

Answer 43

Thanks so much for helping again!

Answer 44

sure thing

Answer 45

Actually, I have 1 more?

Answer 46

Which of the following equations does not represent the Pythagorean Theorem?
image of a triangle whose sides are labels a, b, and c; the corner of sides a and b have a box
A. a2 + b2 = c2
B. a2 - b2 = c2
C. a2 = c2 – b2
D. c2 – a2 = b2

Answer 47

which one do you think it is?

Answer 48

I'll start you off. The Pythagorean Theorem is

\[\Large a^2 + b^2 = c^2\]

Answer 49

I think B

Answer 50

You can isolate \(\Large a^2\) to get this

\[\Large b^2 = c^2-a^2\]

then flip the equation to get

\[\Large c^2-a^2 = b^2\]

Answer 51

B is correct

Answer 52

Find c if a = 3 and b = 4.
Right triangle with sides a, b, and c. Side c is opposite the right angle.
A. c = 7
B. c = 5
C. c = 7/2
D. c = the square root of7

Answer 53

Sorry I'm confused again.

Answer 54

\[\Large a^2 + b^2 = c^2\]

\[\Large 3^2 + 4^2 = c^2\]

solve for c

Answer 55

sqrt(21)

Answer 56

OMG fail.

Answer 57

try it again

Answer 58

It's B

Answer 59

I added wrong-.-

Answer 60

B is correct

Answer 61

Thanks.

Answer 62

np