Find the height of the tree and the breadth of the river.

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°; when he retires 20 m from the bank, he finds the angle to be 30°. Find the height of the tree and the breadth of the river.

Solution:

Let TR be the tree and PR be the width of the river.

The shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 45° to 30°. Find the height of the tower, correct to two decimal places. (2006)

Solution:

In the figure, AB is the tower,
BD and BC are the shadow of the tower in two situations.
Let BD = x m and AB = h m
In ∆ABD,

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• Solve trigonometric:
• Solve: (1 + tan A)/sin A + (1 + cot A)/cos A = 2(sec A + cosec A)
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