Réponse :
1.
[tex]tan(\widehat{ABC}) = \frac{AC}{AB} \\\\AC = AB\times tan(\widehat{ABC})\\AC = 12 \times tan(68)\\AC = 29,7 cm\\\\sin(\widehat{ACB})=\frac{AB}{BC} \\BC = \frac{AB}{sin(\widehat{ACB})} \\BC = \frac{3,5}{sin(25)} \\BC = 8,3 cm[/tex]
2.
[tex]tan(\widehat{ABC}) = \frac{AC}{AB} \\\\tan(\widehat{ABC}) = \frac{5}{12,2} \\\widehat{ABC}=22,3^\circ\\\\cos(\widehat{ACB}) = \frac{AC}{BC}\\ cos(\widehat{ACB}) = \frac{7,4}{10,8}\\\\\widehat{ACB} = 46,7^\circ \\[/tex]
3.
[tex]cos(\widehat{PHB}) = \frac{HB}{HP}\\\\HB = HP \times cos(\widehat{PHB})\\HB = 3 \times cos(20)\\HB = 2,82\;m[/tex]
On peut monter à 2,82 m avec cette échelle.
