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Mathematics
Juila12001:

need help with checking answers and #10 and 12 https://ibb.co/gLvnHx

1 year ago
Shadow:

#10 is a 30-60-90 Triangle Sides Opposite to Angles 90 - 2a 60 - a sqrt 3 30 - a They give the hypotenuse, which is 2x You can solve for y, the side opposite to angle 30 You can do this by dividing (4 sqrt 3) by 2. From 2a -> a \[\frac{ 4 \sqrt 3 }{ 2 } = y\]

1 year ago
Shadow:

y = a as per the 30 60 90 rule The side opposite to the angle 60 is a sqrt 3 So we can do the following, \[a \sqrt 3\] \[a = \frac{ 4 \sqrt 3}{ 2 }\] \[(\frac{ 4 \sqrt 3 }{ 2}) \sqrt 3\] Basically substituting a in. Then we simplify \[\frac{ 4(3) }{2 } = \frac{ 12 }{ 2 } = 6\]

1 year ago
Shadow:

Remember that \[\sqrt x \times \sqrt x = x\]

1 year ago
Shadow:

It seems that your main error though for 10 was putting the wrong values for the sides. You had x for the hypotenuse, 2x for the angle opposite to 60, and x sqrt 3for the angle opposite to 30.

1 year ago
Shadow:

In actuality it's hypotenuse - 2x 60 - x sqrt 3 30 - x

1 year ago
Juila12001:

so for 10 is th e answer 6 or (4 square root 3 over 2) square rooted by 3

1 year ago
Shadow:

Correct, for x. \[y = \frac{ 4 \sqrt 3 }{ 2 }\]

1 year ago
Juila12001:

then where did the 6 come from

1 year ago
Shadow:

\[6 = (\frac{ 4 \sqrt 3 }{ 2 }) \sqrt 3\]

1 year ago
Shadow:

Do you understand?

1 year ago
Juila12001:

oh yea i was just confused bc i thought u meant 6 was the answer

1 year ago
Juila12001:

wait so the answer is 6= (4 square 3 over 2) square ?

1 year ago
Shadow:

\[x = (\frac{ 4 \sqrt 3 }{ 2 }) \sqrt 3\] \[y = \frac{ 4 \sqrt 3 }{ 2 }\]

1 year ago
Shadow:

x also equals 6

1 year ago
Shadow:

6 is better though, since it's simplified.

1 year ago
Juila12001:

so x is 6?

1 year ago
Shadow:

yus

1 year ago
Juila12001:

so u don't have to write 6= (4 square 3 over 2) square ?

1 year ago
Shadow:

nope

1 year ago
Shadow:

All good?

1 year ago
Shadow:

Or is there another one you need help with?

1 year ago
Juila12001:

can check if 8 is correct

1 year ago
Shadow:

|dw:1521605137106:dw|

1 year ago
Shadow:

This means: |dw:1521605198277:dw|

1 year ago
Shadow:

So we can do \[7 = x \sqrt 3\] \[\frac{ 7 }{ \sqrt 3} = x\] \[\frac{ \sqrt 3 }{ \sqrt 3 } \times (\frac{ 7 }{ \sqrt 3 }) = x\] \[\frac{ 7 \sqrt 3 }{ 3} = x\]

1 year ago
Shadow:

\[x = b = \frac{ 7 \sqrt 3 }{ 3 }\]

1 year ago
Shadow:

\[2x = a = 2(\frac{ 7 \sqrt 3 }{ 3 })\]

1 year ago
Shadow:

\[a = \frac{ 14 \sqrt 3 }{ 3}\]

1 year ago
Juila12001:

thank you

1 year ago
Shadow:

No problem. All done?

1 year ago
Juila12001:

yes

1 year ago
Shadow:

Haha, it seems you already had those answers. But you wrote the values wrong for each side. Don't know how that happened xD

1 year ago
Juila12001:

no

1 year ago
Shadow:

|dw:1521605615941:dw| That's what you had on your paper

1 year ago
Shadow:

What's in bold black

1 year ago
Shadow:

I think you know how to do these problems. Just have to set them up correctly.

1 year ago
Juila12001:

yea i just confused setting it up

1 year ago
Shadow:

If you ever need help, I am usually on around this time or a bit later.

1 year ago
Juila12001:

ok thanks

1 year ago
Shadow:

There are some other cool math helpers too. Glad I could help.

1 year ago
Shadow:

When you do need help, just tag me or one of these guys. @Shadow @Vocaloid @563blackghost @TheSmartOne

1 year ago
Juila12001:

ok

1 year ago
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