For this case, we have that by definition, the HF segment is given by:
[tex]Sin (45) = \frac {\sqrt {8}} {HF}\\HF = \frac {\sqrt {8}} {sin (45)}\\HF = \frac {\sqrt {8}} {0.7071}\\HF = 4[/tex]
Now we find the angle FHE, which by definition will be given:
[tex]tg (FHE) = \frac {3} {HF}\\tg (FHE) = \frac {3} {4}\\tg (FHE) = 0.75\\FHE = tg ^ {- 1} (0.75) = 36.86989765[/tex]
Incidentally, the cosine of the FHE angle will be:
[tex]cos (36.86989765) = 0.6755[/tex]
Answer:
0.6755
