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Practice questions for SohCahToa

Solve problems that require manipulation and application of formulas related to perimeter, area, volume, capacity, Pythagorean theorem, trigonometric ratios, income, currency exchange, interest and finance charges

auto-gen

Upper and lower bound

Upper and Lower Bound

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

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

Imperial systems

Imperial Length Conversion

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

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

Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies

Patterns

Patterns — Word Problem

Evaluating algebraic expressions

Evaluating Algebraic Expressions

Solving one - step equations:  x + a = b

1-step Equations

1-step Equations — Word Problem

Demonstrate an understanding of the Pythagorean theorem

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Demonstrate an understanding of primary trigonometric 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

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

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

Solve problems that involve angle relationships between parallel, perpendicular and transversal lines

Parallel and perpendicular lines in linear functions

Applications of linear relations

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Demonstrate an understanding of angles, including acute, right, obtuse, straight and reflex

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Solve problems that involve unit pricing and currency exchange, using proportional reasoning

Rate of change

Applications of rational equations

Converting repeating decimals to fractions

Demonstrate an understanding of simple and compound interest

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Applications of quadratic equations

Scientific notation

Demonstrate an understanding of credit options, including credit cards and loans

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

Geometry, Measurement and Finance 10

Measurement

Number

math

Ex. 1

- Hi! Welcome to this question right here. So this one here you can use whatever you like. Sohcahtoa, you can use sin, cos, tangent as long as you can find the length from b to c, which is from here to here. Okay? 
So how do we know the length from there to there? We only know the angle over here is 22 and this angle here is 15. But if you look in a different way you can actually see there's one right triangle right here. So you can actually find the length from a to b because you kind of know this side's 80 and if you know this angle right here, maybe you can find the length a to b. Then if you look at a bigger scale, if I can just go ahead and treat this big triangle right here, because I know this whole thing right here is 22 plus 15, I can also figure out the a to c. Then I can take the a to c, subtract the a to b and I'll get the b to c. Okay? Kind of weird. Let's actually do it step by step. So let's actually find the length a to b first. So here is my length a to b. So here we go. To find the length a to b, you have to visualize your triangle as actually just this part right here. So you're trying to find the opposite side from this angle 22. This is the opposite, this is the adjacent. So you're going to use tangent. So for the length a to b, I will be using tangent of 22 degrees and the opposite will be the one I'm looking for which is the length a to b divided by the 80 degrees which is the adjacent which is over here. So I'm going to go ahead and calculate that. I've got tangent 22 times 80. Tangent 22 times 80. I'm just gonna write down 32.3. And let's call that centimeters for now. So what about a to c? If you're doing a to c, then you have to look at the triangle like this. Look at it like this. These two angles right here is just 22 plus 15. Twenty-two plus 15, we get 37, right. So from this angle you're looking for the opposite side and you have the adjacent 80 again. So it will just be tangent once again. Using the tangent 37, using these two triangles together is equal to the length of a to c divided by 80 again. So I'm going to go tangent 37 and I'm going to multiply it by 80. A little bit of cross multiplying. I get myself a 60.3 centimeters. So if I know from here to here it's 63 centimeters. So from here to here the blue line is 63 in total and the a to b over here is just 32 roughly, then what will be my b to c? 
Well, just subtract the difference and that's it, right? 
So it just goes 63.2 minus 32.2. . . are they all 0.3s? My bad. All 0.3s. So three and threes are gone. So 63.3-- oh, it's actually 60. I'm really sorry all those mistakes right here. So this is actually 60.3, okay. So, 60.3 minus 32.3 I get myself 28, okay. Sorry about all those scribbles. The final answer should be just 28 centimeters if that was centimeters. Okay? Thanks for watching!

Ex. 2

SOHCAHTOA is actually a memory aid to memorize how to calculate sine, cosine and <a href="[[glossary.html|{"keyword":"Tangent (in Trigonometry)"}]]">tangent</a> of an angle. SOH: sine = opposite over hypotenuse; CAH = adjacent over hypotenuse; and TOA = opposite over adjacent. Besides using them separately, the sine, cosine, and tangent ratios can be used together to solve trigonometry problems.

Use sine ratio to calculate angles and sides (Sin = \(  \frac{o}{h}\) )

Use cosine ratio to calculate angles and sides (Cos =  \(  \frac{a}{h}\)  )

Use tangent ratio to calculate angles and sides (Tan =  \(  \frac{o}{a}\)  )

ASTC rule in trigonometry (All Students Take Calculus)