check the picture below
recall your SOH CAH TOA
[tex]\bf in(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}
\\ \quad \\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}[/tex]
we have,
the angle,
the hypotenuse,
we want the opposite side
which of those fellows have only that? ahhhh it has to be Ms Sine,
so let's ask her
[tex]\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\implies sin(75^o)=\cfrac{x}{100}\implies 100\cdot sin(75^o)=x[/tex]
the opposite side "x", is how tall the tree is
when taking the sine function, make sure your calculator is in Degree mode, since the angle is in degrees
