Answer:
2√3
Step-by-step explanation:
You recognize this as a 30°-60°-90° triangle, so you know the hypotenuse (R) is twice the length of the shortest side (√3).
The magnitude of R is 2√3.
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In case you haven't memorized the ratios for a 30°-60°-90° triangle, you can use trigonometry and the fact that ...
Sin = Opposite/Hypotenuse
sin(30°) = √3/R
R = √3/sin(30°) = √3/(1/2) = 2√3
Of course, doing this on your calculator will give a numerical answer, which you may not want.
The whole ends up being 42 ft².
Area of a triangle = 1/2 * base * height.
So that lil triangle piece is 1/2 * 2 * 3 = 1/2 * 6 = 3
Now we do the rectangle piece. Area of a rectangle = length * width
So that rectangle is 3 * 7 = 21
If you take away those two, you are left with a trapezoid.
Area of a trapezoid is 1/2 * (base 1 + base 2) * height
Base 1 is the width of the rectangle which is 3. Base 2 is the 6. The height is the given 11 feet minus the 7 feet from the length of the rectangle which is 4.
Plug all this in to the formula you get 1/2 * (6 + 3) * 4 = 1/2 * 9 * 4 = 1/2 * 36 = 18.
Now add all of your areas together;
21 + 3 + 18 = 24 + 18 = 42
The required distance would be 17.88 units coordinates A(-4,5) and B(12,13) and the horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.
<h3>What is the distance between two points?</h3>
The distance between two points is defined as the length of the line segment between two places representing their distance.
Given AB with coordinates A(-4,5) and B(12,13).
The formula of the distance between two points is A(x₁, y₁) and B(x₂, y₂) is given by: d (A, B) = √ (x₂ – x₁)² + (y₂ – y₁) ².
x₁ = -4, y₁ = 5
x₂ = 12, y₂ = 13
distance = √ (12 – (-4))² + (13 – 5)²
distance = √ (12 + 4)² + (8)²
distance = √ (16)² + (8)²
distance = √ (256 + 64)
distance = √320
distance = 17.88 units
The horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.
Learn more about the distance between two points here:
brainly.com/question/15958176
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