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Two trees A and B are on the same side of the river. From a

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Two trees $A$ and $B$ are on the same side of the river. From a point $C$ in the river the distance of the tree $A$ and $B$ is $250 m$ and $300 m$ respectively. If the angle $C$ is $4 5^{\circ}$ , find the distance between the trees.

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Two trees $A$ and $B$ are on the same side of the river. From a point $C$ in the river the distance of the tree $A$ and $B$ is $250 m$ and $300 m$ respectively. If the angle $C$ is $4 5^{\circ}$ , find the distance between the trees.

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Text solutionVerified

I n △ A BC

∠ C = 45

AC = 250 m

BC = 300m

Applying the cosine rule

a^{²} = b^{²} + c^{²} - 2 b c cos A

so,

A B^{²} = A C^{²} + B C^{²} - 2 A CBC cos C

= 25 0^{²} + 30 0^{²} - 2 x 250 x 300 x cos 45

A B^{2} = 46433.98

A B = 215.5 m

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Question Text	Two trees $A$ and $B$ are on the same side of the river. From a point $C$ in the river the distance of the tree $A$ and $B$ is $250 m$ and $300 m$ respectively. If the angle $C$ is $4 5^{\circ}$ , find the distance between the trees.
Answer Type	Text solution:1
Upvotes	150

Two trees A and B are on the same side of the river. From a point C in the river the distance of the tree A and B is 250 m and 300 m respectively. If the angle C is 45∘, find the distance between the trees.

Text solutionVerified

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Two trees $A$ and $B$ are on the same side of the river. From a point $C$ in the river the distance of the tree $A$ and $B$ is $250 m$ and $300 m$ respectively. If the angle $C$ is $4 5^{\circ}$ , find the distance between the trees.