While travelling from one station to another , a car travels `75 "km north"` , `60 "km north - east"` and `20 "km east"`. The minimum distance between the two station is

Options

A. `72 km`
B. `112 km`
C. `132 km`
D. `155 km`

Answer

C

Explanation

`x = 60 cos 45^(@) + 20`
`= (60)/(sqrt(2)) + 20 = ( 30 sqrt(2) + 20)km`
`y = 75 + 60 sin 45^(@)`
`= 75 + (60)/(sqrt(2)) = (75 + 30 sqrt(2)) km`
`S = sqrt(X^(2) + Y^(2))` `= sqrt((20 + 30 sqrt(2))^(2) + (75 + 30 sqrt(2))^(2))`
`= sqrt((62.4)^(2) + (117.4)^(2))`
` = 132 km`