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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

Welcome to **nub****trek**.

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

**Just keep tapping** (or clicking) on the content to continue in the trail and learn. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen. continue

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

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Right-Triangles

» All shapes of straight lines can be analyzed as combination of **right-triangles**.

» A right triangle is given by

→ **1** parameter (angle) specify "class of similar-right-triangles"*Note: trigonometry is about specifying the ratio of sides in reference to one angle.*

→ An additional parameter (a side) specify a right-triangle

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

Right angled triangles play a significant role in orthogonal components of quantities with directions and orthogonal components of circular rotation.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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In this page, the importance of right angled triangles in application is explained.

Starting on learning about the importance of Right Angled Triangle in applications.

Before going into details of right angled triangles, students need to understand one application scenario for the same.

A person walks `3` meter north and continues in the same direction for another `4` meter. What is the distance he has to walk to return back to the starting position?

- `3+4 = 7`
- distance is not `3 + 4`

Since the person walks towards north all the time, the answer is '`3+4`'. *Two directional quantities add up in magnitude if they are in same direction.*

A person walks `3` meter north and continues towards east for another `4` meter. what is the distance he has to walk to return back to the starting position?

- `3+4 = 7`
- distance is not `3 + 4`

Since the person walks in different directions, the answer is 'distance is not `3+4`'. *Two directional quantities do not add up in magnitude if they are not in same direction.* The result magnitude will be smaller to the magnitudes of the quantities being added.

A person walks `1` unit at angle `24^@` and then continues to walk `2.3` unit at angle `43^@`.

The problem is illustrated in figure. How this can be solved to find the result?

- Principles of right angled triangles can help to solve
- cannot solve using right angled triangles

The answer is "calculate using right angled triangles"

The first walk of `1` unit at `24^@` is considered as hypotenuse of right angle triangle. The triangle is specified by three parameters 1. right angle 2. given angle 3. length of one side.

The same for the vector `2.3` unit at angle `43^@`, consider that as a right angled triangle. This two can be used to find the sides for the result `bar(OP)`.

How to find `bar(OP)`?

- Add components along x-axis
- Add components along y-axis
- Combine x & y axes components using Pythagoras theorem
- All the above in sequence

Answer is 'All the above in sequence' as evident from the figure.

The distances covered at different angles is a good example of directional quantities. Principles and properties of Right angled triangles are useful to solve problems like that.

Where "sides of right angled triangles" are used in practice?

• Area of a quadrilateral is sum of area of two triangles. Any polygon can be handled as sum of triangles.

• Any triangle can be considered as combination of two right angled triangles.

• Directional quantities are best represented in orthogonal components. The orthogonal components are the legs of the right angled triangles.

• Some Directional quantities have their basis in rotational elements. An example is the induced electric current in a wire that rotates in a magnetic field. The angular speed of rotation is constant, and the directional quantity, derived out of it at a given angle `theta`, is a leg of the right angled triangle defined by `theta`.

• Length of a leg of a right angled triangle, as a function of angle, serves as a mathematical model for analysis.

Students may skip these if these are not easy to understand now. When you use the trigonometry in applications, you may return to refer and understand the above.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Application of Right-Angled-Triangle: ** Application can be classified into

• orthogonal components of quantities having direction.

• orthogonal components of quantities with circular rotation.

• mathematical model for analysis.

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

*your progress details*

Progress

*About you*

Progress

Before going into details of right angled triangles, students need to understand one application scenario for the same.

A person walks 3 meter north and continues in the same direction for another 4 meter. What is the distance he has to walk to return back to the starting position?

equals;equal

3+4 = 7

distance; not

distance is not 3 + 4

Since the person walks towards north all the time, the answer is 3+4 . Two directional quantities add up in magnitude if they are in same direction.

A person walks 3 meter north and continues towards east for another 4 meter. what is the distance he has to walk to return back to the starting position?

equals;equal

3+4 = 7

distance; not

distance is not 3 + 4

Since the person walks in different directions, the answer is 'distance is not 3 plus 4 '. Two directional quantities do not add up in magnitude if they are not in same direction. The result magnitude will be smaller to the magnitudes of the quantities being added.

A person walks 1 unit at angle 24 degree and then continues to walk 2.3 unit at angle 43 degree .How this can be solved to find the result?

principles; help

Principles of right angled triangles can help to solve

cannot; can not

cannot solve using right angled triangles

The answer is "calculate using right angled triangles"

The first walk of 1 unit at 24 degree is considered as hypotenuse of right angle triangle. The triangle is specified by three parameters. First - right angle. Second - given angle. Third - length of one side. The same for the vector 2.3 unit at angle 43 degree, consider that as a right angled triangle. This two can be used to find the sides for the result line O P. How to find line O P?

x axis;x-axis

Add components along x-axis

y axis;y-axis

Add components along y-axis

combine;Pythagoras;theorem

Combine x and y axes components using Pythagoras theorem

above; sequence

All the above in sequence

Answer is 'All the above in sequence' as evident from the figure.

The distances covered at different angles is a good example of directional quantities. Principles and properties of Right angled triangles are useful to solve problems like that.

Where "sides of right angled triangles" are used in practice? ;; Area of a quadrilateral is sum of area of two triangles. Any polygon can be handled as sum of triangles. ;; Any triangle can be considered as combination of two right angled triangles. ;; Directional quantities are best represented in orthogonal components. The orthogonal components are the legs of the right angled triangles. ;; Some Directional quantities have their basis in rotational elements. An example is the induced electric current in a wire that rotates in a magnetic field. The angular speed of rotation is constant, and the directional quantity, derived out of it at a given angle theta , is a leg of the right angled triangle defined by theta . ;; Length of a leg of a right angled triangle, as a function of angle, serves as a mathematical model for analysis. Students may skip these if these are not easy to understand now. When you use the trigonometry in applications, you may return to refer and understand the above.

Right angled triangles play a significant role in orthogonal components of quantities with directions and orthogonal components of circular rotation.

Reference is given.