Question

In triunghiul MNP, N=45°, P=30°, MA perpendicular pe NP, A apartine lui NP, iar MP = 12 cm.
Calculati AP^2+ MN^2​

Answer 1

ΔMAP - dr. in A

m(∡MPA) = 30° => MA = MP/2 = 6 cm

ΔMAP - dr. in A => AP² = 108 => AP = 6√3 cm ;

ΔMAN - dr. in A

m(∡MNA)= 45° => ΔMAN - dr. is

ΔMAN - dr. in A => MN² = 72 => MN = 6√2 cm ;

AP² + MN² = (6√3)² + (6√2)² = 108 + 72 = 180 cm