Area of Non Right Angle Triangle

Introduction on area of non right angle triangle:

The triangles other than the right triangle may be scalene triangle or isosceles triangle. The area of triangle, when all the sides are given is found by using the Heron’s formula. The other method for finding the area of the polygon is when the base and the height of the triangle are given. In the following article we will calculate the area of the non right angle triangle.

Area of Non Right Angle Triangle:

The formula for finding the area of the triangle with all the three sides known is calculated by using the Heron’s formula,

Heron’s formula = `sqrt [s(s-a)(s-b)(s-c)]`

`s = (a + b + c)/2`

The most common formula for calculating the area of the triangle = bh/2

Where, b is the base length and h is the height of the triangle.

The formula for finding the area of an equilateral triangle = `(sqrt 3* a^2)/2`

The formula for calculating the area when two sides and the opposite angle is known is = (ab sin C)/2

Example Problems on Area of Non Right Angle Triangle:

1. Find the area of the triangle if the two sides are 5cm and 7cm, the opposite angle to these sides is 35 degrees.

Solution:

Area formula = (ab sin C)/2

= (5*7* sin 35)/2

= `(35* sin 35)/2`

= `35* 0.574/2`

= 20.09/2 = 10.04 cm^2.

2. Find the area of the triangle with the sides 6cm, 7cm, 9cm.

Solution:

Area of the triangle =` sqrt [s(s-a)(s-b)(s-c)]`

`s = (a + b + c)/2`

= (6+7+9)/2

= 22/2

= 11

Area = sqrt [11(11-6)(11-7)(11-9)]

= sqrt [11*5*4*2]

= sqrt [11*40]

= `sqrt [440]`

= 20.98 cm^2.

I have recently faced lot of problem while learning Right Triangles, But thank to online resources of math which helped me to learn myself easily on net.

Practice problems on area of non right angle triangle:

1. Find the area of the triangle with height 7cm and base 6cm.

Solution: 21 cm^2.

2. Find the area of the triangle with sides 9cm and 11 cm and the angle opposite to them is 42 degrees.

Solution: 33.12 cm^2.

3. Find the area of a equilateral triangle with the side length of 5cm.

Solution: 21.65 cm^2

Narrator, Narrative and Narration

Narrator, narrative and narration are three of the most important terms in English literature. Let’s understand each of the three terms along with examples in this post.

Narrator:  A narrator is the voice that tells a story. The narrator is not the author except in autobiographies. When the narrator is also a character in the story, the narration is done in first person. The narrator can also be created as a third person narrator by the author. Let’s have a look at two examples for better understanding.

Example 1: “I bought at Fisher Price rocker for my friend’s child. Her child is about to be eight months next year and a Fisher Price rocker was a perfect choice for him. I was really happy for her and her baby. But, unfortunately her husband was not in the town to share the experience of parenthood with her.” – Here, the narrator is a first-person narrator.

Example 2: “Mary has started shopping from online stores and has experienced affordable and quality shopping together. She got Johnson baby kit for her baby as Johnson baby kit is considered as the most trusted of brands. She also bought some dresses from Little Kangaroo India collection. And the best part is she got good discount while buy dress from Little Kangaroo India brand.” – Here, the narrator is a third-person narrator.

Narrative: The narrative is the story or the way the events are prepared and presented. Narrative can be classified into various forms such as narrative through speech, writing, songs, film, television and more. The term narrative is also used as a synonym for story.

Narration: Narration means the way that a story is told. Narration can be presented both from outside and being within it. As mentioned earlier, if the narrator is within the story, it becomes a first-person narrative and the narrator is telling the story from inside. On the other hand, when the narrator is outside the story, it becomes a third-person narrative where the narrator talks from outside the story.

These are the basics about narrator, narration and narrative in a story.  

Random Variable X

Introduction to random variable:

The arithmetical value  of a variable is defined by an event,that variable is known as random variable.Random variable may be discrete or continuous.Discrete random variables contains the positive integer values that may exist between zero and infinity.Common example for discrete random variable is when we toss a coin,the possibility of getting head is the positive integer.In continuous random variable the value may range between zero and one sometimes it may be non-integer value.

Random Variable X
random variable x problem 3:

Select the number at random from 12 to 18. What is the probability for select the number is odd?

Solution

The random variables x of the above experiment is 12,13,14,15,16,17,18

i)Take P(A) is the probability of the odd number occur.

The random variable x of odd numbers are 13,15,17.So n(A)=3

Total outcomes n(S)=7

So P(x)=`(n(A))/(n(S))`

=`3/7` .

random variable x problem 4:

Select the number at random from 12 to 18. What is the probability for select the number is even?

Solution

The random variables x of the above experiment is 12,13,14,15,16,17,18

i)Take P(x) is the probability of the even number occur.

The random variable x of even numbers are 12,14,16,18.So n(A)=4

Total outcomes n(S)=7

So P(x)=`(n(A))/(n(S))`

=`4/7` . Please express your views of this topic Convert Decimals to Fractions by commenting on blog.

Random Variable X

random variable x problem 3:

What is the probability of getting a head when a coin is tossed?

Step 1:

The random variable Y contains two possibilities they are head and tail
Step 2:

The random variable is denoted by p(y)

Step 3:

The probability for getting a head is as follows

p(y)=`(n(A))/(n(S))`

Step 4:

The random variable y gives

`p(Y)= 1/2`

random variable x problem 4:

What is the probability of getting a tail when a coin is tossed?

Step 1:

The random variable Y contains two possibilities they are head and tail

Step 2:

The random variable is denoted by p(y)

Step 3:

The probability for getting a tail is as follows

p(y)=`(n(A))/(n(S))`

Step 4:

The random variable y gives

`p(y) =1/2`

Integer Practice

Introduction of integer practice:

We know that integers have positive and negative numbers. Each negative numbers is matching with a positive number the similar distance from 0 on a number line. Example: -6,-5,-4,-3,-2,-1,0,+1,+2,+3,+4,+5,+6. We can write them down like this: {…,-3,-2,-1, 0,1,2,3}. Here we are going to learn how to practice integers.

Rules:

Rules for adding integers:

Rule 1:  Suppose if add the same sign, add the two numbers and put their common sign.

(+62) + (+14) = +76 (-29) + (-13) = -42.

Rule 2:  Suppose if we add the different signs, we need to find the difference between the two numbers and put the sign of the number.

(+15) + (-8) = +7 (+9) + (-30) = -21

Rules for subtracting integers:

Rule 1: Commonly every subtraction problem can be rewrite as a corresponding addition problem,

Use the follow rule: To subtract an integer, add its reverse.

1. (-8) – (+9) = The opposite of +9 is –9. Change sign to opposite: (-8) + (-9) = -17 using Integer addition rules

Switch rule 1 to subtract signed numbers:

Step 1: First, change double negatives to a positive.

Step 2: Get a sum of terms with same signs and keep the given sign, using the sign in front of the number as the sign of the number.

Step 3: Get the difference when the terms have different signs and use the sign of the larger numeral. Understanding Radian Measure is always challenging for me but thanks to all math help websites to help me out.

Practice Problems for Integers:

Practice adding positive integers:

We know that addition is the basic operations in math. Here we are going see some practice problems of addition.

Example 1:

23+21.

Solution:

Here both the numbers are positive .And then addition process is done here.

The result  is 23+21 = 44.

Practice adding negative integers:

-256 +-24.

Solution:

When we take this above problem, we have both negative numbers. And we need to find the total of these two numbers. And negative 256 plus negative 24 equals negative 280.

The result is -280.

Practice subtraction integers:

Turn the subtraction symbol into addition and get the reverse of the second number. Then take the problem as an addition problem.

Example 1:

Integer subtraction:

-128+18.

Solution:

Here the first number is negative and the next number is positive. The subtraction procedure is finished. The biggest number sign will appear to answer

The result is -128+18= 110.

Unit Circle with Tangent

Introduction:

The Unit circle is used to understanding the sins and cos of angles to find 90 degree triangle. Unit circleis radius is exactly one. The center of circle is said to be origin and its perimeter comprises the set of all points that are exactly one unit from the center of the circle while placed in the plane.It s just a circle with radius ‘one’.

Unit Circle Standard Equation:

In unit circle: The distance from the origin point(x,y) is by using Pythagorean Theorem.

Here radius is one So, The expression should becomes =1

Take square on both sides then the equation  becomes,

X2+y2 =1

Positive angles are found using counterclockwise from the positive x axis

And negative angles are found anti clockwise from negative axis. Please express your views of this topic what is a line segment by commenting on blog.

The Graph of the Unit Circle with Tangent Function:

The  correspondence of  `theta` with tan  ` theta` , Here ` theta` is a real number  so, from the definition of tangent function,

tan `(theta)` = Sin `(theta)` /cos`(theta)`

Values for the tangent function can be created.  Above  is the unit circle.  Remember that the sine, cosine, and tangent are all built from this picture.  Hence, they are called circular functions.

These values are the angle measure (the value closest to the circle) and the tangent values.  So starting with angle 0, notice that the tangent value is 0.

Equivalent Systems of Equations

Introduction:

An equivalent system of equation is a system of equations in which both systems have same solution but they may have different numbers of equations.

Systems of Linear Equations

It is a set of algebraic expressions in the form:


a11x1 + a12x2 + .....................+a1nxn = b1


a21x1 + a22x2 + .....................+a2nxn = b2


am1x1 + am2x2 + .....................+amnxn = bm


xi are the unknowns, (i = 1, 2, ..., n).
aij are the coefficients, (i = 1, 2, ..., m), (j = 1, 2, ..., n).
bi are the independent terms, (i = 1, 2, ..., m).
m, n ; m > n, or, m = n, or, m < n.
The number of equations need not equal the number of unknowns.
aij and bi  .
When n is less, it is usual to assign the unknowns with the letters x, y, z, t, ...
When bi = 0, for all i, the system is called homogeneous.

Equivalent systems of equations are obtained by elimination if:


The value of coefficients is zero.
Two equal rows are present.
Two rows are proportional to each other.
A row is formed by linear combination of others. Looking out for more help on Algebra Mixture Problems in algebra by visiting listed websites.

Equivalence Criteria

The resulting system is equivalent if both members of an equation of a system are added or subtracted by the same expression.
The resultant system is equivalent, if both members of the equations of a system are multiplied or divided by a number other than zero,
The resultant system is equivalent, if an equation of a system is added or reduced by another equation of the same system.
The resultant system is equivalent, if an equation in a system is replaced by another equation that results from adding the equations of a system previously multiplied or divided by nonzero numbers,
If the order of the unknowns of a system or order of the equations is changed, it is another equivalent system.

Want to Learn How to Divide

Introduction of want to learn how to divide:-

In mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that is the inverse of multiplication.I like to share this Elementary Row Operations with you all through my article.

Specifically, if c time’s b equals a, written:

c x b = a

Where b is not zero, then a divided by b equals c, written:

`a/b` = c.

In the above expression, a is called the dividend. (Source: Wikipedia)

Step by Step Process of Want to Learn How to Divide 20 by 2:-

In following steps for want to learn how to divide 20 by 2

Step 1:-

-------
2 | 20

In the above equation 2 is divisor and 20 is dividend. In the divisor has two decimal numbers put the value dividend of  20.

Step 2:-

10
-------
2 | 20
20
---------
0
--------

Normally divide the values one by one the right value has 0 means directly divided by two digits. In 2 x 10 = 20 the divisor number 2 is multiplied with 10 to get an answer 20.In 20 is equal to 20. So use the values then subtracts the value and get remainder is 0.Please express your views of this topic trigonometry help by commenting on blog.

Example Problems for Want to Learn How to Divide:-

Problem 1:-

How to divide 54 by 2

Solution:-

In following steps for want to learn how to divide 54 by 2

Step 1:-

-------
2 | 54

In the above equation 2 is divisor and 54 is dividend. In the divisor has two decimal numbers put the value dividend of  5 .

Step 2:-

2
-------
2 | 54
4
---------
14

In 2 x 2 = 4 the divisor number 2 is multiplied with 2 to get an answer 4. In 4 is less than from 5.So use the value then subtract the value and get 1.

Step 3:-

27
-------
2 | 54
4
---------
14
14
--------
0
--------

In 2 x 7 = 14 the divisor number 2 is multiplied with 7 to get an answer 14. In 14 is equal to 14. So use the values then subtracts the value and get remainder is 0.



Problem 2:-

How to divide 48 by 2

Solution:-

In following steps for want to learn how to divide 48 by 2

Step 1:-

-------
2 | 48

In the above equation 2 is divisor and 48 is dividend. In the divisor has two decimal numbers put the value dividend of  48.

Step 2:-

2
-------
2 | 48
4
---------
8

In 2 x 2 = 4 the divisor number 2 is multiplied with 2 to get an answer 4. In 4 is equal to  4. So use the value then subtract the value and get 0. Put the next value 8.

Step 3:-

24
-------
2 | 48
4
---------
8
8
----------
0
----------

In 2 x 4 = 8 the divisor number 2 is multiplied with 4 to get an answer 8. In 8 is equal to 8. So use the values then subtracts the value and get remainder is 0.