Answer:
42 meters
Step-by-step explanation:
Given
See attachment for complete question
Required
Calculate distance FC
FC is calculated as:
[tex]FC = Path\ 1 + Path\ 2[/tex]
Where
[tex]Path\ 1 = FB[/tex]
[tex]Path\ 2 = BC[/tex]
Considering [tex]\triangle FEB[/tex], we have:
[tex]FB^2 = FE^2 + BE^2[/tex] --- Pythagoras theorem
Where
[tex]FE = FD - BA[/tex]
[tex]FE = 22m - 15m[/tex]
[tex]FE = 7m[/tex]
and
[tex]BE = CD - CA[/tex]
[tex]BE = 32m - 8m[/tex]
[tex]BE = 24m[/tex]
So:
[tex]FB^2 = FE^2 + BE^2[/tex]
[tex]FB^2 = 7^2 +24^2[/tex]
[tex]FB^2 = 49 +576[/tex]
[tex]FB^2 = 625[/tex]
Take square roots of both sides
[tex]FB = 25[/tex]
So:
[tex]Path\ 1 = 25[/tex]
Considering [tex]\triangle BAC[/tex], we have:
[tex]BC^2 = BA^2 + AC^2[/tex] --- Pythagoras theorem
Where:
[tex]BA = 15[/tex] and [tex]AC = 8[/tex]
So, we have:
[tex]BC^2 = 15^2 + 8^2[/tex]
[tex]BC^2 = 225 + 64[/tex]
[tex]BC^2 = 289[/tex]
Take square roots of both sides
[tex]BC = 17[/tex]
So;
[tex]Path\ 2= 17[/tex]
Recall that:
[tex]FC = Path\ 1 + Path\ 2[/tex]
[tex]FC = 25 + 17[/tex]
[tex]FC = 42[/tex]
