SOLUTION: Q#1: An equilateral triangle has one vertex at the origin , other vertex on x-axis and the third in the first quadrant. Find the slope of its sides. Plz mail me the solution

Question 890626: Q#1: An equilateral triangle has one vertex at the origin , other vertex on x-axis and the third in the first quadrant. Find the slope of its sides.

Plz mail me the solution of the question with all the complete step by step. plz i again say with all the steps.
Thanks....
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the slope of the left side of the triangle will be + sqrt(3).

the slope of the right side of the triangle will be equal to - sqrt(3).

this is derived as follows:

an equilateral triangle has each angle equal to 60 degrees.

the base of the triangle will be horizontal on the x-axis.

the left side of the triangle will have a slope that is equal to the tangent of 60 degrees.

the tangent of 60 degrees is equal to the sine of 60 degrees divided by the cosine of 60 degrees.

the sine of 60 degrees is equal to sqrt(3)/2.

the cosine of 60 degrees is equal to 1/2.

the tangent of 60 degrees is therefore equal to sqrt(3)/2 divided by 1/2 which makes the tangent of 60 degrees equal to sqrt(3).

the right side of the triangle has an angle of minus 60 degrees.

since the tangent of minus 60 degrees is equal to minus the tangent of 60 degrees, then the slope of the right side of the equilateral triangle is equal to minus sqrt(3)/2.

the geometric rationale for determining the slope of the left side of your triangle and the slope of the right side of your triangle is shown in the attached picture.

$$$

the equation of the base of your triangle is y = 0.

the equation of the left side of your triangle is y = sqrt(3).

the equation of the right side of your triangle is y = -sqrt(3) + b.

the b is the y-intercept of the right side of your triangle.

if b is equal to 0, the left side of your triangle and the right side of your triangle intersect at the origin and you have no triangle because the length of each side will be equal to 0.

a picture of that is shown below.

$$$

if you want the length of the base of your equilateral triangle to be equal to 30, then you need to make the height of your triangle equal to 30 * sqrt(3).

when you do this, the length of the base of your triangle will be equal to 30, as will the length of the other two sides of your triangle.

a picture of that is shown below.

$$$

whatever you want the length of each side of your triangle to be, then just make b in the equation equal to that length * sqrt(3).

for example, if you want the length of the sides to be 20, then the equation becomes y = -sqrt(3) + 20 * sqrt(3).

you only do this to the right side of your triangle.

that's the one with the negative slope.

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