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 `A` and `B` be the trees an `C` be a point in the river.

Then, `C A=250 m, CB=300 m and angle A C B=45^{circ}.`

Let `A B=x metres`
.
Applying costine formula on `triangle A C B`, we get


`Cos C frac{a^{2}+b^{2}-c^{2}}{2 a b} `

`Rightarrow cos 45^{circ}=frac{(300)^{2}+(250)^{2}-x^{2}}{2 times 300 times 250}`

`Rightarrow frac{1}{sqrt{2}}=frac{90000+62500-x^{2}}{150000} `

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