Question

Can someone please help I have been stuck on this and 1 more problem for 4 days now..
A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims, that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.

Answer 1

THIS IS THE OTHER ONE IF ANYONE COULD HELP IT WOULD BE GREATLY APPRECIATED! (:
There are two fruit trees located at (3,0) and (–3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.

Answer 2

Why not draw (at random) a couple of triangles, labeling various components, and then try applying the Law of Sines and the Law of Cosines to each situation? By experimenting, you're likely to learn quite a bit about which Law is the better to use in which situations.

Answer 3

Regarding your second problem: Please look up key words such as "equation of an ellipse" or "foci of an ellipse" when you're unsure of what to do. When I looked up the latter, I found this site:

https://www.google.com/search?q=foci+of+an+ellipse&rlz=1C1CHFX_enUS461US461&espv=210&es_sm=122&tbm=isch&tbo=u&source=univ&sa=X&ei=3CUOU_a5K4LBoAS7xICADA&ved=0CCkQsAQ&biw=1360&bih=673

from which I captured a bit of it that's most relevant to your posted question:

Answer 4

Please sketch your situation (vertices at (-3,0) and (3,0) ) and then draw in a rough ellipse based upon those two vertices.

Now compare your drawing to the one I posted, above.

You yourself must choose an appropriate length for the "minor axis," which in the drawing I posted is labelled "b."

When you're done sketching your ellipse, please post it (use the Draw utility). I'd be glad to give you helpful feedback regarding what you've done and what you need to do next.

Answer 5

So (3,0) and (-3,0) would be my focuses correct? and (0,0) would be my center? @mathmale

Answer 6

Actually, they'd be your vertices. See my previous post, from above:

Please sketch your situation (vertices at (-3,0) and (3,0) ) and then draw in a rough ellipse based upon those two vertices.

Have you sketched this ellipse in such a way that you can share the image with me?

Have you looked at the illustration I shared with you? See above. Its name is ellipses.png.

Answer 7

@mathmale this is what I have so far. what is my next step?