Question 828971
We have a 30 60 90 triangle.
The ratio of the side lengths are {{{1 : sqrt(3):2}}}
where 1/2 is opposite the 30 degree angle, {{{sqrt(3)}}}
is opposite the 60 degree angle.
In our scenario, the short distance across the river
corresponds to the side opposite the 30 degree angle.
The distance along the bank, 34.4M , is the side opposite
the 60 degree angle.
We can set up proportion
{{{(side opposite 30)/side opposite 60)}}}={{{1/(sqrt(3))}}}={{{x/34.4}}}
where x represents the distance across the river.
So do cross products for {{{1/(sqrt(3))}}}={{{x/34.4}}}
{{{sqrt(3)*x}}}={{{34.4*1}}}
divide each side by {{{sqrt(3)}}}
{{{x}}}={{{34.4/sqrt(3)}}}
multiply the right side by {{{(sqrt(3))/(sqrt(3))}}}
{{{x}}}={{{(34.4*sqrt(3) )/3}}}