Equation of a line by using pythagoras theorem

Pythagorean theorem is important triangle formula which is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle in British English). It states:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).we use this in most trigonometry examples

The theorem can be written as an equation:

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.


Question:-

Find the distance between two points R(5,1) and S(-3,-3)

Answer:-
Let's solve this by using a graph,so that we can draw the line by using the given points and we can make use of Pythagoras theorem to find the distance between them.

(RS)²=(RT)²+(ST)²

(RS)²=4²+8²

(RS)²=16+64

(RS)²=80

RS = √80

similarly ,we can find all points having an x-coordinate of 2 whose distance from the point 2 1 is 5

A Simple Trigonometric Problem.

Trigonometric equation can be solved using trigonometric identities and find the value of x/radian/degree

Topic : Trigonometric Equation

In Trigonometric functions - Sine, Cosine, tan's value are found as explained below.

Problem : Solve tan 2x = 3 tan x and find x in degrees

Solution :
tan 2x = 3 tan x
we have tan 2x = 2 tan x/1 - tan² x
2 tan x/1 - tan² x = 3 tan x
2 tan x = 3 tan x (1 - tan² x)
2 tan x = 3 tan x - 3 tan³ x
3 tan³ - 3 tan x + 2 tan x = 0
3 tan³ - tan x = 0
or tan x (3 tan² x - 1) = 0
tan x = 0 or 3 tan² - 1 = 0
x = 0 or tan² = 1/3
x = 0 or tan x = ± 1/√3
x = 0⁰
or
tan x = +1/√3 ; x = 30⁰ or x = 180⁰ + 30⁰ = 210⁰ and
if x = -1/√3 ; x = 180⁰ - 30⁰ = 150 or 360⁰ - 30⁰ = 330⁰

So x = 0⁰, 30⁰, 150⁰, 210⁰, 330⁰


If required values can be converted into radians.
For more help write to our trigonometric help.