Question

Please could you calculate the length of a to f please

Answer 1

Check the picture below.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{40}\\ o=\stackrel{opposite}{60} \end{cases} \\\\\\ AC=√( 40^2 + 60^2)\implies AC=√( 1600 + 3600 ) \implies \boxed{AC=√( 5200 )} \\\\[-0.35em] ~\dotfill`

`\tan(25^o )=\cfrac{\stackrel{opposite}{FC}}{\underset{adjacent}{60}} \implies \boxed{60\tan(25^o)=FC} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} \textit{ the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{A F}\\ a=\stackrel{adjacent}{√(5200)}\\ o=\stackrel{opposite}{60\tan(25^o)} \end{cases} \\\\\\ (A F)^2= (√(5200))^2 + (60\tan(25^o))^2\implies A F^2\approx 5200+27.98^2 \\\\\\ A F\approx√(5200+27.98^2)\implies \boxed{A F\approx 77.349~cm}`