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Master 45-45-90 Triangle Rules: Solve Expressions Easily

NL.SO.1202A1

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

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NL.SO.1202G2

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

NL.SO.1202G3

Similar triangles

Similar polygons

Isosceles and equilateral triangles

NL.SO.1202G4

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

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

NL.SO.1202G5

Parallel and perpendicular lines in linear functions

Angles in a circle

Chord properties

Tangent properties

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

NL.SO.1202M1

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

NL.SO.1202M2

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

NL.SO.1202M3

Upper and lower bound

Upper and Lower Bound

Converting repeating decimals to fractions

NL.SO.1202M4

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

NL.SO.1202N1

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

Joint and combined variation

Money related questions in linear equations

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

Percent of a number

Percent of a Number

percent of a number – Word Problem

Percent of a Number  Fraction Percent

Percent of a Number Integer Percent 

Percent of a number number With Decimal Percent 

Percent of a Number  Three Digits Number Percent

Adding and multiplying percents

Add and Multiply Percents — Word Problem

Add and Multiply Percents – Word Problem

Applied Mathematics 1202

Measurement

Number

math

Intro

Intro to special right triangles: 45-45-90 and 30-60-90

Ex. 1

<p>- Hi, welcome to special<br />
[inaudible 00:00:02].<br />
So we're dealing with special triangles, okay. So, here it says, "If the angle is 45 degrees, find the exact value of the following expressions." So, what we have here is this. We've got the, a three and a sine square of the theta here. So, if this is 45 degrees, what happens is there's a three and you take the sine and there's a square here and this is the theta 45. Now, don't worry about the square right now. And you're not squaring the 45. See, the problem with the trig is that they like to put the square here, rather than actually here. Technically, this thing right here, is actually saying this: sine 45 and then you put a square sign like that. But they don't do it this way. They actually put it here, I don't know why. So, let's go ahead and figure this out, but you can use your calculator but remember, 45 degrees is one of a special triangle. So, what that means is, you have 90 degrees, right. And this is 45 and this is 45. So, remember, if you happen to have this special triangle, the ratio's going to be one, one and a root two for the hypotenuse. So, what that means is, you're going to have the sine 45 is going to turn out to be opposite over hypotenuse like that. So, you're going to get yourself one over root two for this part right here or this part right here. So, I'm just going to continue to work right here. Sine 45 is just one over root two and then you square that. So, if you square the one, just let me do a little work here a little bit. Square root of one is double one. If you take the root to square it, you get the two. And three times one over two, the final answer is just three over two. And that is your final answer for this one. Thanks for watching.</p>
