Please see diagram:
A right triangle has 3 main trigonometric ratios. These ratios are the relationships between different sides of the triangle, how large one side is compared to the other side. If you have every angle, in degrees, of a triangle, then you can figure out the relation between the lengths of the three sides. Additionally, you can figure out the value of the angles, given the sides of the triangle.
In the diagram, we are interested in the trigonometric ratios with respect to angle
a.
You see in the diagram that sine, cosine, and tangeant are described as their ratios: (one way to remember: SohCahToa
sine = opposite / hypotenuse
cosine = adjacent / hypotenuse
tangeant = opposite / adjacent.
cosecant, secant, and cotangents are just the reciprocals of these ratios:
cosecant = 1 / sin
secant = 1 / cosine
cotangeant = 1 / tangeant
The exponential form of 64 is
.
The square root of 64 is 8. So 8 x 8 = 64.
The area of the lawn is 6144 square ft.
So you need to come up with a perfect square that works for the x coefficients.
like.. (2x + 2)^2
(2x+2)(2x+2) = 4x^2 + 8x + 4
Compare this to the equation given. Our perfect square has +4 instead of +23. The difference is: 23 - 4 = 19
I'm going to assume the given equation equals zero..
So, If we add subtract 19 from both sides of the equation we get the perfect square.
4x^2 + 8x + 23 - 19 = 0 - 19
4x^2 + 8x + 4 = - 19
complete the square and move 19 over..
(2x+2)^2 + 19 = 0
factor the 2 out becomes 2^2 = 4
ANSWER: 4(x+1)^2 + 19 = 0
for a short cut, the standard equation
ax^2 + bx + c = 0 becomes a(x - h)^2 + k = 0
Where "a, b, c" are the same and ..
h = -b/(2a)
k = c - b^2/(4a)
Vertex = (h, k)
this will be a minimum point when "a" is positive upward facing parabola and a maximum point when "a" is negative downward facing parabola.
The base length is 5.5 cm.
Explanation:
Area of triangle = base x height x 1/2
Let b cm be the base length of the triangular flag.
22 = b x 8 x 1/2
22 x 2 ÷ 8 = b
b = 44 ÷ 8
b = 5.5