Question 1005706
Find the acute angle that is formed by the line {{{ y-sqrt(3x) +1 = 0 }}} and the x-axis.
-------------
{{{ y-sqrt(3x) +1 = 0 }}}
That's not a line, it's a curve.
You can find the slope of the line tangent to the curve at y = 0:
---
{{{ y-sqrt(3x) +1 = 0 }}}
Find the x-intercept:
{{{ y = sqrt(3x) -1 = 0 }}}
{{{sqrt(3x) = 1}}}
3x = 1
x = 1/3
----------------
y' = {{{(1/2)*3/sqrt(3x)}}}
@ x = 1/3:
y' = (3/2)
--
The slope 3/2 is the tangent of the angle.
--> angle =~ 56.31 degs