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Mastering Pythagorean Theorem Applications in Real Life

NY.GEO-G.C.1

Central angles and proofs

NY.GEO-G.C.2a

Central and inscribed angles in circles

NY.GEO-G.C.2b

NY.GEO-G.C.5

auto-gen

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

NY.GEO-G.CO.1

Line symmetry

Angles in a circle

Chord properties

Circles and circumference

Circle properties

Arcs of a circle

Areas and sectors of circles

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

NY.GEO-G.CO.10

Classifying triangles

Isosceles and equilateral triangles

NY.GEO-G.CO.11

Area and perimeter of parallelograms

2d shapes area and perimeter of parallelogram

2d shapes area and perimeter of parallelograms

NY.GEO-G.CO.12

Perpendicular bisectors

NY.GEO-G.CO.13

Inscribed angles and proofs

NY.GEO-G.CO.2

Rotational symmetry and transformations

Introduction to transformations

NY.GEO-G.CO.3

Horizontal and vertical distances

NY.GEO-G.CO.6

Congruence and congruent triangles

NY.GEO-G.CO.7

Triangles congruent by SSS proofs

NY.GEO-G.CO.8

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

NY.GEO-G.CO.9

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

NY.GEO-G.GMD.1

Surface area and volume of prisms

Surface area and volume of cylinders

Surface area and volume of cones

NY.GEO-G.GMD.3

Surface area and volume of pyramids

NY.GEO-G.GMD.4

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

NY.GEO-G.GPE.1a

Conics - Circle

NY.GEO-G.GPE.1b

NY.GEO-G.GPE.4

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Introduction to vectors

NY.GEO-G.GPE.5

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

NY.GEO-G.GPE.6

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

NY.GEO-G.GPE.7

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

NY.GEO-G.MG.1

Scale diagrams

NY.GEO-G.MG.2

Word problems of polynomials

NY.GEO-G.SRT.1

Enlargements and reductions with scale factors

NY.GEO-G.SRT.2

Similar triangles

NY.GEO-G.SRT.4

Pythagorean theorem

Pythagorean Theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

NY.GEO-G.SRT.5

Similar polygons

NY.GEO-G.SRT.6

Use sine ratio to calculate angles and sides (Sin = o / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

NY.GEO-G.SRT.7

Use cosine ratio to calculate angles and sides (Cos = a / h)

Cofunction identities

NY.GEO-G.SRT.8

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

NY.GEO-G.SRT.9

Area of triangles: 1/2 a*b sin(C)

math

Intro

Hi, welcome to this question right here. So we&apos;ve got a plane, kinda flew from a point A starting from here, it went to the point B for 300 meters, then for some reason a 90&deg; turn and went to a point C for another 400 meters, okay. And we're trying to figure out how far is a plane from point A which means you're now here, we're looking for how far are you, from where you start, okay? 
So that's the side right there, and as you can see, that's a right triangle, okay? 
So it looks like you're missing the X over here which is the hypotenuse. So Pythagorean theorem, here it comes one more time. So C&sup2; = a&sup2; + b&sup2;, 
and once again the hypotenuse is always the longest side of the right triangle. So you have to put your X&sup2; here, but for A and B it's your choice, you can put your a for this one or this one, b for this one or that, it doesn't matter so let's just plug it in 300 and square that plus the 400 and square that. Now I'm just gonna find out the answer on the right hand side. Squaring the both sides and adding them together we get ourselves the 250,000, and my X square is still missing. So to figure out the X, I will square root both sides. Why do I do that? 
Because it allows me to cancel the square sign right there. So I end up with just the X and I just have to square root my 250,000 then I get myself the 500 and it looks like it's meter, and that's the answer for this question. Thanks for watching.

We will need to apply Pythagorean Theorem often in our daily life. In this lesson, we will focus on tackling some Pythagorean Theorem word problems. 

Word problems of pythagorean relationship

Applying the Pythagorean Theorem