The library in Ben's town is 3 blocks east and 7 blocks north of his house. He finds a short cut by walking diagonally from his house to the library. How much shorter is the shortcut than walking the blocks?

There is 2.38 shorter is the shortcut than walking the blocks.

The distance walking the blocks

Distance = 3 + 7

= 10

Now

The distance via  pythagorean theorem

 = 7.62

Now the difference of distances

 = 10 - 7.62

 = 2.38 units

Therefore we can conclude that There is 2.38 shorter is the shortcut than walking the blocks.

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The answer to your question is 2.4 units shorter.

Step-by-step explanation:

Data

3 blocks east and 7 blocks north.

Process

1.- Calculate the distance walking the blocks

     distance = 3 + 7

     distance = 10

2.- Calculate when walking diagonally using the pythagorean theorem

     distance² =  3² + 7²

     distance² = 9 + 49

     distance² = 58

     distance = 7.62

3.- Calculate the difference of distances

     Δd = 10 - 7.62

     Δd = 2.38 units

(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