Side wall planes

Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls.

Correct answer:

S =  5217.801 cm2
V =  24681.8833 cm3

Step-by-step explanation:

c=30 cm α=24+20/60=37324.3333  β=45+30/60=291=45.5   t1=tanα=tan24.333333333333° =0.452218=0.45222 t2=tanβ=tan45.5° =1.017607=1.01761  d2 = a2+b2+c2 u12 = a2 + c2 u22 = b2 + c2  tan α = a : u2 = t1  t12   (b2+c2) = a2  tan β = b : u1 = t2 t22   (a2+c2) = b2  t12   (b2+c2) = a2 t22   (a2+c2) = b2  t22   (t12   (b2+c2)+c2) = b2  t22 (t12 (x+c2)+c2)=x 1.01760739297212 (0.45221787913672 (x+302)+302)=x  0.788234x=1122.561608  x=0.788234131122.56160768=1424.1474246  x=1424.147425  b=x=1424.147437.7379 cm a=t12 (b2+c2)=0.45222 (37.73792+302)21.8012 cm  S=2 (a b+b c+a c)=2 (21.8012 37.7379+37.7379 30+21.8012 30)=5217.801 cm2
V=a b c=21.8012 37.7379 3024681.8833 cm3   Verifying Solution:  u1=a2+c2=21.80122+30237.0849 cm u2=b2+c2=37.73792+30248.2094 cm A=π180°arctan(a/u2)=π180°arctan(21.8012/48.2094)=37324.3333  B=π180°arctan(b/u1)=π180°arctan(37.7379/37.0849)=291=45.5 

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