NEED HELP WITH THESE QUESTIONS ASSAP

1) 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. Who is correct, Maurice, Johanna, or both? Use complete sentences and justify your answer, using measurements when necessary.
2)An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.
3) There are two fruit trees located at (4,0) and (−4, 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.
4) A pipe needs to run from a water main, tangent to a circular fish pond. On a coordinate plane, construct the circular fishpond, the point to represent the location of the water main connection, and all other pieces needed to construct the tangent pipe. Submit your graph. You may do this by hand, using a compass and straight edge, or by using a graphing software program.
5) Two pillars have been delivered for the support of a shade structure in the backyard. They are both nine feet tall and the cross sections of each pillar have the same area. Explain how you know these pillars have the same volume without knowing whether the pillars are the same shape.

1.Your answer would be, For example, the Triangular section of a lawn is named ABC, The sides are name ABC, respectively as the opposite of the angles, with the similar letters. Like Side A is opposite angle (a). The missing side length is B, To get this, Maurice, used the Law of Cosines. In order to use this, Maurice need to have two sides, and angle between them, that is given to solve for the missing lengths, which is Sides A, and C, and an angle B. Johanna used the Law of Sines, in which, she need two angles, and an opposite sides, that should be given to find the missing Length, which is Angle B, and C, and Side C. So, Since both Laws use the remaining were given, The use of both, will result in a similar measurements.

2.draw a perpendicular line from the directrix passing through the focus, this will be the line of symmetry. The vertex(h, k) will be located on the line half way between the focus and directrix. The distance from the focus to the vertex is called the focal length, call it a. The then equation is (x - h)^2 = 4a(y - k) the equation can be manipulated to y = 1/4a(x - h)^2+ k.

4. We choose a fish pond of radius 3 centered at (x, y) = (0, 3). The equation of the circle is ...

(x -0)^2 +(y -3)^2 = 3^2

x^2 +(y -3)^2 = 9

At this location it is easy to draw a radius along the y-axis to a point of tangency at the origin. That radius is a vertical line, so the tangent line will be perpendicular--a horizontal line.

A horizontal line through the origin has equation y = 0, and its point of intersection with this circle is (0, 0).

Hope this helps you!!

Mark brainleast!!