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  tanα=a:u2=t1  t12 (b2+c2)=a2  tanβ=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=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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