il 304

ΗΒ = √(24^2 - 6^2) = 6·√15 cm

ΗA = √(9^2 - 6^2) = 3·√5 cm

AB = ΗΒ - ΗΑ= (6·√15 - 3·√5) cm

Th Carnot:

24^2 = 9^2 + (6·√15 - 3·√5)^2 - 2·9·(6·√15 - 3·√5)·COS(α°)

COS(α°) = - √5/3----> α = 138.19°

Th Carnot:

9^2 = (6·√15 - 3·√5)^2 + 24^2 - 2·(6·√15 - 3·√5)·24·COS(β°)

COS(β°) = √15/4-----> β = 14.48°

γ° = 180° - (α° + β°)----> γ = 180° - (138.19° + 14.48°)

γ° = 27.33°

CB = a = 24 cm AC = b = 9 cm AB = c CH = e = 6 cm HA = d

CB²= (HA +AB)² +CH²= (d + c)² + e² --> 24² = (d + c)² + 6²
AC²= AH²+ CH² = d²+e² = b² ---> 9² = d² + 6²

c = 3 sqrt(5) (2 sqrt(3) - 1), c≈16.530,

d = 3 sqrt(5) , d≈6.7082

th dei seni... + A+B+C = pi

c/sinC = a /sinA = b/sinB --> 3 sqrt(5) (2 sqrt(3) - 1)/sinC = 24 /sinA = 9/sinB

A≈2 (3.14159 n_1 + 1.20593), B≈2 (3.14159 n_2 + 0.12634), C≈-6.28319 n_1 - 6.28319 n_2 + 0.477047, n_1 element Z, n_2 element Z

A^= 2*1.20593 --> 138.19° (degrees)   per n1 =0
B^ = 2*0.12634 --> 14.4786° (degrees)  per n2 = 0
C^ = 0.477047 --> 27.3328° (degrees)  per n1 = n2 = 0  

altezza AH = h

base BC = b

lati obliqui AB = AC = l

b = 2A/h = 160*2/20 = 16 m 

l = √h^2+(b/2)^2 = √20^2+8^2 = 4√29 m 

perimetro 2p = 8√29+16 = 8(2+√29) m 

angolo A = 2*arctan 8/20 = 2*arctan 2/5

angoli B e C = arctan 5/2

hl = 2A/l = 320/4√29 = 80/√29 = (80*√29)/29 m 

AH = √AC^2-CH^ = √81-36 =3√5

BH = √24^2-6^2 = 6√15

AB = 6√15-3√5 = 3(2√15-√5)

angolo CAH = arctan 6/3√5 = arctan 2√5 /5 = 41,81°

angolo CAB = 180°-angolo CAH = 180-41,81 = 138,19°

angolo ABC = arctan 6/(6√15) = arctan √15 /15 = 14,48° 

angolo ACB = 180-(138,19+14,48) = 27,33°

9 sin (180° - A^) = 6

180° - a = arcsin*(2/3)

A = 180° - arcsin*(2/3) = 138°

BC/sin A^ = AC/sin B^

sin B^ = AC/BC sin A^ = 9/24 * 2/3 = 1/4

B^ = arcsin* (1/4) = 14.5°

C^ = 180° - (15 + 138)° = 27°

AB = sqrt(24^2 - 6^2) - 9 cos A^ =

= sqrt (540) - 9 sqrt (1 - 4/9) =

= 3 rad(60) - 9/3 rad(5) = 6 rad(15) - 3 rad(5) =

= 3 rad(5) (2 rad(3) - 1)

AC = 40/sin 34,85 = 70,00 cm

AH = 10√7^2-4^2 = 10√33 = AB*sen 73,40°

AB = 10√33/sen 73,40° = 62,360 cm 

AH/BH = tan 73,40° = 3,3544

BH = AH/3,3544 = 10√33/3,3544 = 17,125 cm 

BC = 40+17,125 = 57,125 cm