Question

Fie mnp un triunghi cu m(unghiului m)=90 daca tg n=radical din 3 aflati sin p

Answer 1

N
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M________________P

tg N = MP/MN=rad3 =>MN=MP/rad3=MPrad3/3
t.Pitagora : MN^2 + MP^2 = NP^2
3MP^2/9 + MP^2 = NP^2
12MP^2 = 9NP^2 |:3
4MP^2 = 3NP^2 |radical
2MP=NPrad3 =>NP=2MPrad3/3
sin P = MN/NP = MPrad3/3 • 3/2MPrad3
sin P = 1/2 => m(<P)=30°