Question 158903
You can also solve by TRIGO FUNCTIONS:
Remember: {{{H[T]=x}}} unknown; {{{S[T]=22ft}}}
{{{h[ys]=3ft}}}; {{{s[ys]=4ft}}}
Since both forms a right triangle, we can use trigo function {{{SINE}}} = {{{opp/hyp}}}:
{{{sin(alpha) =opp/hyp=h[ys]/s[ys]}}}
{{{sin(alpha)=3/4}}}
{{{alpha=sin^-1(0.75)}}}
{{{alpha=48.59deg}}} -----> the same angle the TREE forms
Therefore,
{{{sin(alpha)=H[T]/S[T]}}}
{{{sin(48.59)=H[T]/22}}}
{{{H[T]=sin(48.59)(22ft)}}}
{{{H[T]=16.5ft}}} --------------------------> Height of the Tree
Thank you,
Jojo