The total mass of two cows is 96 kilograms. The mass of one of the cows is at least 20 kilograms more than the other. The mass of the lighter cow is more than 35 kilograms. What are the three possible masses of the heavier cow?

9514 1404 393

  {58, 59, 60} kg

Step-by-step explanation:

Let x represent the mass of the heavier cow. Then the mass of the lighter cow is 96 -x.

The inequalities regarding the relative masses are ...

  x ≥ 96-x +20 . . . . . the heavy cow is at least 20 kg heavier

  96 -x > 35 . . . . . . . the lighter cow is more than 35 kg

__

Adding x to the first inequality makes it ...

  2x ≥ 116

  x ≥ 58

Adding x-35 to the second inequality makes it ...

  61 > x

So the mass of the heavier cow must be in the range ...

  58 ≤ x < 61

Possible whole-number masses for the heavier cow are ...

  58 kg, 59 kg, 60 kg

(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