BGS - 05. Geometry and Measures Flashcards
Circles
Area = A
Circumfurence = C
Diameter = **d
Radius = r**
Tangent
Chord
Segment
Arc
Sector
Area = within the circle walls
Circumfurence = length around the edge of circle
Diameter = even distance across circle
Radius = distance from center of circle to outer edge
Tangent = straight line laid against the outer edge of the circle touching one point
Chord = Straight line between 2 points within the circle circumfurence
Segment = Shaded area between a chord line or diameter line and the circle circumference
Arc = Section of the circumfurence line, typically between where 2 radial lines meet on the outer edge, the length between the radial points
Sector = Space between 2 radial lines within the circufurence wall
1
Calculating the Circumference of Circles
C = 2 π r
or
C = π d
π = Pi
Pi = 3.14159
As 2x Radius is the same as Diameter, this is why there are 2 methods
2
Calculating the Area of Circles
A = π r²
What is area of a circle with radius of 15cm
A = π 15²
π x 15 x 15
A = 709.9cm²
3
Perimeters and Areas of Circle Sectors
To determine a sector area size and arc length, use the formula to determine area and circumfurence of a circle first and work backwards
I.e. you want the length of an arc and sector area size for a ¼ of a circle with a radius of 1.5m
A = π r²
A = π x (1.5 x 1.5)
Area = 7.07m²
C = 2 π r
C = 2 x π x 1.5
Circumfurence = 9.42m
We want to determine a ¼ sector size so we can multiple the above answers by ¼
7.07 x ¼
Area of Sector = 1.77m²
For the perimeter of the sector however, we multiple the circumfurence by ¼ to obtain the arc lenght MUST remember to add 2x radius which form the other part of the perimeter
Arc = 9.42 x ¼
Arc = 2.356m
Circumfurence of sector = arc + 2r
2.356 + (1.5 x 2)
Cicumfurence of sector = 5.356m
¼ = 0.25
4
Perimeters and Areas of Circle Sectors
A full circle has 360°
If the angle of a sector is known and the circles radius, you can determine its perimeter and area;
Area = A x sector angle ➗ 360
Perimeter = (C x sector angle ➗ 360) + 2r
4
Polygons
Area of a rectangle
Area = Length x Width
Circumfurence of rectangle
Cirumfurence = (2 x L) + (2 x W)
5
Calculating angles of Triangle
Internal angles of a triangle add up to 180°
Therefore;
a + b + c = 180°
With 2 of the angles given, it is therefore possible to determine the missing angle;
c = 180° - (a + b)
6
Calculating angles of Triangle
If a straight line of a triangle edge were extended outwards, the angle within the triangle and the angle outside (external angle) to the straight edge will total 180°
Therefore,
c + d = 180°
Pythagoras Theorem
a² + b² = c²
Where C is always the longest side
The sum of the 2 smaller squares equals the sum of the largest square
Given the length of any 2 sides, it is possible to calculate the length of the 3rd side
a =√(c² - b²)
b = √(c² - a²)
c = √(a² + b²)
7
Vectors
Vectors are measures that have magnitude and direction
A velocity is a vector measure
i.e. wind strength and direction
If only wind strength were reported, this would be a scaler
Wind reported as 330°/14kts = velocity (vector)
Wind reported as 14 kt = scalar
12
Vectors
vectors represented on a graph are seen as positive or negative.
Triangle of Velocities
You can use triangle of velocities when factoring in wind speed and direction to calculate aircraft resulting heading and speed.
Line AB = aircraft heading and speed
Line BC = Wind vector
Line AC = resulting line due to addition of wind vector
Measuring line AC will give the aircraft speed and measuring the angle will give the aircraft heading
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