Two trees, A and B are on the same side of a river. From a point C in the river the distance of trees A and B are 25 m and 300 m respectively. If the angle `C` is `45^0` , find the distance between the trees `(u s e\ sqrt(2)=1. 44)`

Explanation

Let PQ is a river. Two trees A and B are on a bank of this river. The distance of A and B from a point C in the river are 250m and 300m respectively.
`therefore` CA=250 m, CB=300 m Given that `angleACB=45^(@)`
`cosC=(CA^(2)+CB^(2)-AB^(2))/(2CA.CB)`
`cos45^(@)=(250^(2)/2+300^(2)-AB^(2))/(2 xx 250 xx 300)`
`rArr (2 xx 250 xx 300)/(sqrt(2))=62500+90000-AB^(2)`
`rArr AB^(2)=152500-75000 xx sqrt(2)`
`=152500 - 75000 xx 1.44`
`=152500-108000`
=44500
`rArr AB=sqrt(44500)`
`=210.95` km Ans.