Question

how do I solve for x and y in this picture? There should be a square root in both answers. https://media.glynlyon.com/g_geo_2012/11/groupi39.gif

Answer 1

It's not by cosign or tangent, I've tried

Answer 2

\[\tan 30=\frac{ x }{ 7}\]

Answer 3

tan 30 =\[\frac{ \sqrt{3} }{ 3 }\]

Answer 4

I know that the short side is the long side divided by sqrt3, and the hypotenuse is twice the short side, but the way the answer is formatted to be filled in for x is _ _ _ (sqrt) _ and _ _ _ _ (sqrt) _ for y.

Answer 5

solve for x and then take this to do the sin , do you need anymore help?

Answer 6

The sine of an angle is equal to the opposite side over the hypotenuse, so:
\[\sin 30 = x/y\]Sin 30 is equal to 1/2 so:
\[1/2=x/y\]so:
\[2x=y\] Since this is a right triangle, apply the pythagorean theorem:
\[49 + x^2 = y^2\]Now you can try solving this system of equations for x and y.

Answer 7

...I still don't get it

Answer 8

What would I put in for x or y in the Pythagorean theorem?

Answer 9

Using the substitution method, plug in 2x for the y. You can then solve for the x.

Answer 10

I'm still not getting the correct answer. You mean put it as 49 + x^2 = 2x, right?

Answer 11

I tried that but then got 24.5x=x^2
Do I divide from there?

Answer 12

49 + x^2 = 4x^2

Answer 13

ohhh, okay, let me try that again, then

Answer 14

No, I still get 7/sqrt3, and that doesn't work for this format

Answer 15

It has to fit as _ _ _ sqrt _

Answer 16

I'm just going to call the school tomorrow, this is ridiculous. I'm out, bye.

Answer 17

Okay, so, you're actually supposed to rationalize the denominator, because you can't have a sqrt under there. So multiply both the numerator and denominator by sqrt3 in this can, and then I get 7sqrt3/3 or 7/3 sqrt 3. then to find y, just multiply it by 2