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There is a small island in the middle...

There is a small island in the middle of a 100m wide river and a tall tree stands on the island. `P` and `Q` are points directly opposite to each other on two banks and in line with the tree. If the angles of elevation of the top of the tree from `P` and `Q` are respectively `30o` and `45o` , find the height of the tree.

A

`50(sqrt3-1)`

B

`50(sqrt3+1)`

C

`100(sqrt3+1)`

D

`100(sqrt3-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Draw the figure as per the description given in the problem. Two right triangles are formed. Use appropriate trignometric ratios by considering each of the triangle and find the hieght of tree.
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Knowledge Check

  • Two posts are 4 m apart. Both posts are on same side of a tree. If the angles of depression of these posts when observed from the top of the tree are 45 and 60° respectively, then what is the height of the tree?

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    B
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    C
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