Angle HEG is 37 because the sum of all angles f a triangle is 180 and 180-90-53=37
The same way we find the angle GEF
2) the triangles are similar because they have the same shape, however they are located differently
the angle measures are equal
has a scaling factor
3)to solve the scale we can divide two measures that are equivalent on this case
[tex]\frac{16}{12}=\frac{4}{3}[/tex]
4)
we can solve HG and then calculate GF using the scale
HG
[tex]\begin{gathered} \sin (37)=\frac{HG}{12} \\ \\ HG=12\sin (37) \\ \\ HG=7.22 \end{gathered}[/tex]
multiplying by the factor we find GF
[tex]\begin{gathered} 7.22\times\frac{4}{3}=HG \\ \\ HG=9.62 \end{gathered}[/tex]
HF is the sum of HG abd GF, then
[tex]\begin{gathered} 7.22+9.62=HF \\ HF=16.84 \end{gathered}[/tex]
