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triangle was A,B,C angle B 56 and side length little c is 14 little b is 17 solve triangle using Law of sines (SSA case)

Solving for angle C we have

sin C / 14  = sin 56 / 17

sin C  = [14 * sin 56] / 17  

arcsin [ (14 * sin 56) / 17 ]  ≈ 43°

And angle A   =   180 - 56 - 43  ≈   81°

And  side a  =

a / sin 81  =  17/ sin 56   →  a = 17sin 81/sin 56 ≈ 20.25

To see if we have a second triangle, C might also  be  180 - 43  = 137°

However......when we add this to the known angle of 56°, we get more than 180°....so....only one triangle is possible

a = 20.25        b = 17       c  =  14

A = 81            B = 56       C = 43

Hi Chris,

No it is definitely not an identity.  The question does not say 'prove'

I just took it as a solve for x question.  :)

\(7\frac{7}{9} + 2\frac{1}{9} \\~\\ = 7 + \frac{7}{9} + 2 + \frac{1}{9} \\~\\ = 7 + 2 + \frac{7}{9} + \frac{1}{9} \\~\\ = 9 + \frac{8}{9} \\~\\ = 9 \frac{8}{9}\)

I hope this made sense :)

\(\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} \\~\\ \frac{\sin 56}{17} = \frac{\sin C}{14} \\~\\ \frac{14\sin 56}{17} = \sin C \\~\\ \arcsin{(\frac{14\sin 56}{17})} = C \\~\\ C \approx 43.058^{\circ}\)

Since there are 180 degrees in every triangle,

180 = A + B + C

A = 180 - B - C

A ≈ 180 - 56 - 43.058

A ≈ 80.942º

All that's left to find is side a.

\(\frac{\sin 56}{17} \approx \frac{\sin 80.942}{a} \\~\\ (a)\frac{\sin 56}{17} \approx \sin 80.942 \\~\\ a \approx \frac{17\sin80.942}{sin56} \\~\\ a \approx 20.250\)

Recap:

A ≈ 80.942º          a ≈ 20.25

B = 56º                   b = 17

C ≈ 43.058º            c = 14

*edit* I put c = 4 instead of c = 14

Need to find two square roots of 25

Don bought 0 apples.

He bought 12 appels but 0 apples.

Unless Don is being sneaky and he bought apples without telling anyone about it.

It can not be 516 because it has to be less than 4 not 4

Steak. l wish didn't like it so much.

Express 0.034 x 10^7 in scientific notation 

=3.4 x 10^5

Solve for x:
2 + sqrt(2 x + 3) = sqrt(6 x + 7)

Raise both sides to the power of 2:
(2 + sqrt(2 x + 3))^2 = 6 x + 7

Subtract 6 x + 7 from both sides:
-7 - 6 x + (2 + sqrt(2 x + 3))^2 = 0

-7 - 6 x + (2 + sqrt(2 x + 3))^2 = 4 sqrt(2 x + 3) - 4 x:
4 sqrt(2 x + 3) - 4 x = 0

Simplify and substitute y = sqrt(2 x + 3):
 4 sqrt(2 x + 3) - 4 x = 6 + 4 sqrt(2 x + 3) - 2 (sqrt(2 x + 3))^2 = -2 y^2 + 4 y + 6 = 0:
-2 y^2 + 4 y + 6 = 0

The left hand side factors into a product with three terms:
-2 (y - 3) (y + 1) = 0

Divide both sides by -2:
(y - 3) (y + 1) = 0

Split into two equations:
y - 3 = 0 or y + 1 = 0

Add 3 to both sides:
y = 3 or y + 1 = 0

Substitute back for y = sqrt(2 x + 3):
sqrt(2 x + 3) = 3 or y + 1 = 0

Raise both sides to the power of two:
2 x + 3 = 9 or y + 1 = 0

Subtract 3 from both sides:
2 x = 6 or y + 1 = 0

Divide both sides by 2:
x = 3 or y + 1 = 0

Subtract 1 from both sides:
x = 3 or y = -1

Substitute back for y = sqrt(2 x + 3):
x = 3 or sqrt(2 x + 3) = -1

Raise both sides to the power of two:
x = 3 or 2 x + 3 = 1

Subtract 3 from both sides:
x = 3 or 2 x = -2

Divide both sides by 2:
x = 3 or x = -1

2 + sqrt(2 x + 3) ⇒ 2 + sqrt(3 + 2 (-1)) = 3
sqrt(6 x + 7) ⇒ sqrt(7 + 6 (-1)) = 1:
So this solution is incorrect

2 + sqrt(2 x + 3) ⇒ 2 + sqrt(3 + 2 3) = 5
sqrt(6 x + 7) ⇒ sqrt(7 + 6 3) = 5:
So this solution is correct

The solution is:
Answer: |x = 3

x - 80% = 90

what is x

x - 80%x = 90

20%x = 90

0.20x = 90

x =90 / 0.20

x =450

x - 64% =72

what is x

x - 64%x =72

36%x = 72

0.36x = 72

x =72 / 0.36

x = 200

x - 15% = 146.54

what is x

x - 15%x = 146.54

85%x =146.54

0.85x =146.54

x =146.54 / 0.85

x = 172.4

I can show you a couple different "ways" of doing it. (They all accomplish the same thing though.)

\(x - \frac{80}{100} = 90 \\~\\ x=90+\frac{80}{100} \\~\\ x=\frac{454}{5}=90.8\)

---------------------------------------------------------------------------------

\(x - \frac{64}{100} = 72 \\~\\ x-0.64=72 \\~\\ x=72+0.64=72.64\)

---------------------------------------------------------------------------------

\(x - 15\% = 146.54 \\~\\ x - 0.15 = 146.54 \\~\\ x = 146.54 + 0.15 =146.69\)

Thank you!

\(\frac{x}{7} = \frac{30}{100} \\~\\ x = (7)(\frac{30}{100}) \\~\\ x = 210/100 = 2.1\)

Law of Sines:

\(\frac{\sin A}{a} = \frac{sin B}{b} = \frac{\sin C}{c}\)

Plug in what you know.

\(\frac{\sin56}{49} = \frac{\sin C}{58} \\~\\ \frac{58\sin56}{49} = \sin C \\~\\ \arcsin({\frac{58\sin56}{49}}) = C \\~\\ C \approx 78.905^{\circ}\)

So since we know that there are 180º in every triangle,

180 ≈ 56 + 78.905 + B

B ≈ 180 - 56 - 78.905

B ≈ 45.095º

3.4 * 10^9

ok 

thanks u guys

I just realized that you might have meant:

\(\sqrt{\frac{270.4}{10}} \\~\\ = \sqrt{\frac{676}{25}} \\~\\ = \frac{\sqrt{676}}{\sqrt{25}} \\~\\ = \frac{26}{5}\)

Which comes out to a nice even 5.2, so that is possibly what you meant.

I feel like we should consider the clapping cat as a new member of its own. :P

I feel like we should consider the clapping cat as a new member of its own. :P

\(\frac{40}{x} = \frac{75}{100} \\~\\ 40 = \frac{75x}{100} \\~\\ 4000 = 75x \\~\\ 53\frac{1}{3} = x\)

1/3 =100%?

ok thats good. no new member yet, just letting people know to look out for th cat and know wut it means.