We use the laws of cosine in SSS and SAS triangles. With that being said lets say we have a triangle ABC. We already know each side is a,b,c but what we don't know is what C Equals. We would use the laws of cosine c2 = a2 + b2 − 2ab cos(C) to find C.
We can use the law of sines when we know 2 angles and 1 side and want to get the side opposite a known angle. Looking at triangle ABC we know what A, C, and b equals but what we don't know is what a and c equals. Law of sines would come into play to solve the triangle.
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
3)
- first I wrote out the formula for an horizontal ellipse x^2/a^2+y^2/b^2=1.
- You want a^2−b^2=3^2
I used the 3−4−5 right triangle to make:a=5,b=4so c=3 and usex^2/5^2+y^2/4^2=1
- For the hyperbola We already know that c=3. I decided a=2 . 3^2=2^2+b^2. 9=4+b^2. 5=b^2. b= 2.23.... Next, to create the equation, we substitute what we know to the equation x^2/a^2 - y^2/b^2 = 1.
- x^2/2^2 - y^2/2.23^2 = 1.
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) The formula used to find the volume of a pillar is v = pi r^2h. They are both 10 feet tall and they both have the same cross sections meaning that they have the same radius. Plugging the values into the formula gives you the same volume.
