A rectangular suitcase measures 2 ft high by 3 ft long by 1 ft wide. Can an umbrella that is 42 inches long be packed in the suitcase? Justify your answer.

yes (see below)

Step-by-step explanation:

Use diagonal of a cuboid equation:  

where l is the length, w is the width and h is the height

ft

x 12 = 44.90 inches

As 42 < 44.90, the umbrella can be packed in the suitcase.

rx and sx

step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47