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Mastering Pythagorean Theorem Applications in Real Life

Solve problems requiring manipulation and application of formulas related to perimeter area Pythagorean theorem

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Evaluating polynomials

Solving polynomial equations

Word problems of polynomials

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)

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Solving literal equations

Demonstrate understanding of Pythagorean theorem identify right triangle situations verify formula apply formula solve problems

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Demonstrate understanding of similarity in convex polygons including regular and irregular polygons

Similar triangles

Similar polygons

Isosceles and equilateral triangles

Demonstrate understanding of primary trigonometric ratios apply similarity to right triangles generalize patterns apply ratios

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

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

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

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

Solve problems involving parallel perpendicular and transversal lines and pairs of angles formed between them

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Parallel and perpendicular lines in linear functions

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Demonstrate understanding of angles draw replicate construct bisect solve problems

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Demonstrate understanding of SI system relationships between units for length, area, volume, capacity, mass, temperature

Upper and lower bound

Upper and Lower Bound

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

Demonstrate understanding of imperial system relationships between units for length, area, volume, capacity, mass, temperature

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Imperial systems

Imperial Length Conversion

Solve and verify problems involving SI and imperial linear measurements including decimal and fractional measurements

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

Solve problems involving SI and imperial area measurements of regular, composite, and irregular 2-D shapes and 3-D objects

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>

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Solve problems involving unit pricing and currency exchange using proportional reasoning

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Direct variation

Identifying direct variations

Inverse variation

Money related questions in linear equations

Rate of change

Applications of linear relations

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Apprenticeship and Workplace Mathematics 10 (MAT421K)

Measurement

Number

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

Estimating square roots