What is distance between points (asin60, 0) and (0,cos30)

We are given two points:

Point A = (asin60, 0)
Point B = (0, cos30)

We use the distance formula to find the distance between these two points. The distance formula is given by:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given coordinates:

x1 = asin60, y1 = 0
x2 = 0, y2 = cos30

Distance = sqrt((0 - asin60)^2 + (cos30 - 0)^2)
= sqrt((asin60)^2 + (cos30)^2)

We now calculate the trigonometric values:

sin60 = sqrt(3)/2
cos30 = sqrt(3)/2

Thus,

asin60 = a * (sqrt(3)/2)
cos30 = sqrt(3)/2

Substituting these values:

Distance = sqrt((a * sqrt(3)/2)^2 + (sqrt(3)/2)^2)
= sqrt((3a^2)/4 + 3/4)
= sqrt(3(a^2 + 1)/4)
= sqrt(3(a^2 + 1)) / 2

Thus, the distance between the given points is:

sqrt(3(a^2 + 1)) / 2