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summary of this topic

Basics of Trigonometry

Basics of Trigonometry

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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

Importance of Right Angled 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.


Keep tapping on the content to continue learning.
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.vector addition basics 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.vector addition first principles 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^@`.
vector addition first principles 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"

vector addition using trigonometric calculations 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.

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