151
angolo ABC = π(1-1/3-1/5 = 7π/15
cos (7π/15) = 0,1045
AC = √( (8√3)^2+20^2-2*20*(8√3)*0,1045) = 64*3+400-320√3*0,1045 = 23,1
semiperimetro p = 8√3+20+23,1 = 56,96 cm
area = √(28,48*(28,48-8√3)*(28,48-20)*(28,48-23,1)) = 137,8 (arrotond. a 138)
152
EB = EC = 2√2
BC = √8+8-2*8*0,866 = 1,464
angolo DEC = 105-(180-30)/2 = 30°
ED = 8+9-2*6√2*0,8668+9-2*6√2*0,866 = 2,30
altezza EH = √8-(1,464/2)^0,5 = 2,673
area ABE = 2^2/2 = 2,0 cm^2
area BCE = b*h/2 = 1,464*2,673/2 = 1,96 cm^2
semiperimetro EDC = (2√2+3+2,30)/2 = 4,066
area EDC = √4,066*(4,066-2,82)*(4,066-3)*(4,066-2,30) = 3,09 cm^2
area totale = 2+1,96+3,09 = 7,045 cm^2
Es. 150.
$8sin\alpha$ è l'altezza del triangolo, quindi
$17*8sin\alpha/2=60$
Pertanto $sin\alpha=15/17$ e quindi
$\alpha=arcsin(15/17)$