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November 10, 2008

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This is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of ‘Right triangle and trigonometric functions’. The mini-lessons here include: Getting started, The Tangent Ratio, Inverse Tangent, Inverse Sine and Cosine, Angles of Elevation and Depression.

- Mathematics > General
- Mathematics > Geometry

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Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.?

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This is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of ‘Right triangle and trigonometric functions’. The mini-lessons here include: Getting started, The Tangent Ratio, Inverse Tangent, Inverse Sine and Cosine, Angles of Elevation and Depression.

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting started.

When it comes to solving word problems, generally we've to break the problem down into smaller parts and solve one part at a time. It is necessary to understand that certain words indicate certain mathematical operations, e.g. "more than", "decreased by", "times" and "ratio of" mean addition, subtraction, multiplication and division respectively. To take a specific example, the ratio of 6 more than x to x would mean (x + 6)/x. A few other things to keep in mind:

= is used for is, are, and equal

< is used for is less/lower than

? is used for is less than or equal to

> is used for is greater/larger than

? is greater than or equal to

()^{2 } is used squared

()^{3 } is used for cubed.

When it comes to solving word problems, generally we've to break the problem down into smaller parts and solve one part at a time. It is necessary to understand that certain words indicate certain mathematical operations, e.g. "more than", "decreased by", "times" and "ratio of" mean addition, subtraction, multiplication and division respectively. To take a specific example, the ratio of 6 more than x to x would mean (x + 6)/x. A few other things to keep in mind:

= is used for is, are, and equal

< is used for is less/lower than

? is used for is less than or equal to

> is used for is greater/larger than

? is greater than or equal to

()

()

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting Started - Right triangle and trigonometric functions.

This mini-lesson introduces and walks you through the basic concepts of the trigonometric functions, right triangle and their relationship. You'll learn it with the help of some examples, practice questions with solution, using video and explanation in own handwriting by the instructor that brings in an element of real-class room experience.

The three primary trigonometry functions are: sin*x*, cos *x*, tan *x*. The input value usually represents an angle. The length of three sides of a right triangle, are simply termed as the ‘opposite’. ‘adjacent’ and ‘hypotenuse’. The values for the trigonometric functions are defined as the value that you get when divided one side by the other side i.e. ratio of one side to the other. E.g. sin *x* = opposite / hypotenuse.

Further you’ll explore, how you can use the ratios of side-length of right triangles to determine the measures of sides and angles. We’ll apply the Pythagorean Theorem, concept of ratio and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. E.g. In a right triangle*ABC*, with sides *a*, *b* and *c*, you need to remember:
*a* = 10 and *b* = 24, then

*c*^{2} = *a*^{2} + *b*^{2} = 10^{2} + 24^{2} = 100 + 576 = 676.

The square root of 676 is 26, so*c* = 26.

This mini-lesson introduces and walks you through the basic concepts of the trigonometric functions, right triangle and their relationship. You'll learn it with the help of some examples, practice questions with solution, using video and explanation in own handwriting by the instructor that brings in an element of real-class room experience.

The three primary trigonometry functions are: sin

Further you’ll explore, how you can use the ratios of side-length of right triangles to determine the measures of sides and angles. We’ll apply the Pythagorean Theorem, concept of ratio and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. E.g. In a right triangle

- Pythagorean theorem:
*a*^{2}+*b*^{2}=*c*^{2} - Sines: sin
*A*=*a*/*c*, sin*B*=*b*/*c* - Cosines: cos
*A*=*b*/*c*, cos*B*=*a*/*c* - Tangents: tan
*A*=*a*/*b*, tan*B*=*b*/*a*

The square root of 676 is 26, so

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - The Tangent Ratio.

Here you’ll learn the definition and concept of The Tangent Ratio, using video and explanation in own handwriting by the instructor.

The tangent ratio is the ratio of leg opposite to an angle of a right angle to the leg adjacent to the angle i.e.

tan = opposite/adjacent.

The tangent ratio for acute angles is constant. Further you will learn how to find the tangent ratio for any angle of right triangle, given the measure of the sides of the triangle.

Here you’ll learn the definition and concept of The Tangent Ratio, using video and explanation in own handwriting by the instructor.

The tangent ratio is the ratio of leg opposite to an angle of a right angle to the leg adjacent to the angle i.e.

tan = opposite/adjacent.

The tangent ratio for acute angles is constant. Further you will learn how to find the tangent ratio for any angle of right triangle, given the measure of the sides of the triangle.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Inverse Tangent.

In this section you’ll learn with the help of some examples with solution; the definition and concept of the Inverse Tangent, using video and explanation in own handwriting by the instructor.

Inverse tangent is opposite of the tangent. Now let us analyze the function*y* = tan *x*. When the positions of *x* and *y* variables are switched, it is known as the inverse tangent function and is denoted by *y* = tan^{-1}*x*. Generally you use tangent for an angle to find the *y*/*x* value. In case of inverse tangent, you'll use the *y*/*x* value to find the angle. The angle that has a tangent of 1 is called the “inverse tangent of 1” and is written tan^{-1}1, which equals 45 degree.

Now explore what will be the measure of the angle, the tangent of which will be -1? This works out to 135° and 315° i.e. in second and forth quadrant.

Note: the value of*y* = tan^{-1} *x* exist, if and only if, tan *y* = *x* where -?/2 is less than y is less than ?/2.

In this section you’ll learn with the help of some examples with solution; the definition and concept of the Inverse Tangent, using video and explanation in own handwriting by the instructor.

Inverse tangent is opposite of the tangent. Now let us analyze the function

Now explore what will be the measure of the angle, the tangent of which will be -1? This works out to 135° and 315° i.e. in second and forth quadrant.

Note: the value of

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Inverse Sine and Cosine.

In this mini-lesson you’ll learn with the help of some examples with solution, the definition and concept of the Inverse Sine and Cosine, using video and explanation in own handwriting by the instructor.

The inverse trigonometric functions (sin^{-1}, cos^{-1}, and tan^{-1}) allow you to find the measure of an angle in a right triangle. All that you need to know is any two sides as well as how to use SOHCAHTOA.

Compare sine with inverse sine (General Difference):

Sine is the ratio of two sides of a right triangle (opposite and hypotenuse). Inverse or sin^{-1} is an operation that uses the same two sides of a right triangle as sine does (opposite over hypotenuse) in order to find the measure of the angle i.e. sin^{-1} is the measure of angle.

Thus the key difference is: although both sine and inverse sine involve the opposite side and hypotenuse of a right triangle, the result of these two operations are different. One operation (sine) finds the ratio of these two sides; the other operation, sine inverse, actually calculates the measure of the angle (using the opposite side and the hypotenuse.

It will be true in the similar way for cos and cos^{-1}. But remember cos is the ratio of two sides of a right triangle (adjacent and hypotenuse).

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this mini-lesson you’ll learn with the help of some examples with solution, the definition and concept of the Inverse Sine and Cosine, using video and explanation in own handwriting by the instructor.

The inverse trigonometric functions (sin

Compare sine with inverse sine (General Difference):

Sine is the ratio of two sides of a right triangle (opposite and hypotenuse). Inverse or sin

Thus the key difference is: although both sine and inverse sine involve the opposite side and hypotenuse of a right triangle, the result of these two operations are different. One operation (sine) finds the ratio of these two sides; the other operation, sine inverse, actually calculates the measure of the angle (using the opposite side and the hypotenuse.

It will be true in the similar way for cos and cos

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Angles of Elevation and Depression.

This mini-lesson introduces and walks you through the basic concepts of the trigonometric functions and explains how you can solve word problems that involve angle of elevation and depression. It should help you to enhance skills to enable applying with the distance formula knowledge, in everyday practical situations and real life applications. You will learn it with the help of some examples, practice questions with solution, using video and explanation in own handwriting by the instructor that brings in an element of real-class room experience.

The angle of elevation is the angle formed by a horizontal line and the line joining an observer's eye or an object to some other object above the horizontal line. On the other hand an angle of depression is the angle formed by a horizontal line and the line joining an observer's eye or an object to some other object beneath the horizontal line. It also covers the steps or method to find angle of elevation or angle of depression when the distance is known, alternatively the method to find out the distance or length, given the angle of elevation or depression. For example, if a tree is 10 feet in height and casts a shadow of length 15 feet, then the angle of elevation from the end of the shadow to the top of the tree is 34°.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

This mini-lesson introduces and walks you through the basic concepts of the trigonometric functions and explains how you can solve word problems that involve angle of elevation and depression. It should help you to enhance skills to enable applying with the distance formula knowledge, in everyday practical situations and real life applications. You will learn it with the help of some examples, practice questions with solution, using video and explanation in own handwriting by the instructor that brings in an element of real-class room experience.

The angle of elevation is the angle formed by a horizontal line and the line joining an observer's eye or an object to some other object above the horizontal line. On the other hand an angle of depression is the angle formed by a horizontal line and the line joining an observer's eye or an object to some other object beneath the horizontal line. It also covers the steps or method to find angle of elevation or angle of depression when the distance is known, alternatively the method to find out the distance or length, given the angle of elevation or depression. For example, if a tree is 10 feet in height and casts a shadow of length 15 feet, then the angle of elevation from the end of the shadow to the top of the tree is 34°.

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Curriki Rating**'C'** - Curriki rating C**'C'** - Curriki rating

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