(Solved): 1) Three forces are applied to a tree sapling, as shown in fig, to stabilize it. If FA=380 ...

1) Three forces are applied to a tree sapling, as shown in fig, to stabilize it. If $$F_A=380\mathrm{N}$$ and $$F_B=255\mathrm{N}$$, find $$F_C$$ in magnitude and direction. a) $${\mathrm{F}}_{\mathrm{C}}=379\mathrm{N},?=141^{?}$$ b) $${\mathrm{F}}_{\mathrm{C}}=255\mathrm{N},?=40^{?}$$ c) $${\mathrm{F}}_{\mathrm{C}}=400\mathrm{N},?=160^{?}$$ d) $$F_C=200\mathrm{N},?=14^{?}$$ 2) Calculate the $$F_A$$ and $$F_B$$ of the support posts of a diving board exerted by a $$56\mathrm{kg}$$ person $$3\mathrm{m}$$ from that post. a) $${\mathrm{F}}_{\mathrm{A}}=?0.25\times 10^3\mathrm{N},{\mathrm{F}}_{\mathrm{B}}=?36\times 10^3\mathrm{N}$$ b) $${\mathrm{F}}_{\mathrm{A}}=?3.58\times 10^3\mathrm{N},{\mathrm{F}}_{\mathrm{B}}=56\times 10$$ c) $${\mathrm{F}}_{\mathrm{A}}=?2.2\times 10^3\mathrm{N},{\mathrm{F}}_{\mathrm{B}}=6.9\times 10^3\mathrm{N}$$ d) $${\mathrm{F}}_{\mathrm{A}}=?1.6\times 10^3\mathrm{N},{\mathrm{F}}_{\mathrm{B}}=2.2\times 10^3$$