A person standing on the bank of river finds that the angle of elevation of the top of a tower on opposite side bank is 45°. Which of the following statement is correct

Breadth of the river is half of the height of the tower
Breadth of the river and the height of the tower are equal
Breadth of the river is twice the height of the tower
None of these

Correct Answer: Breadth of the river and the height of the tower are equal

Explanation:

Let us draw a figure below as per given question.
Let AB = h m be the height of the tower, BC = x m be the breadth of the river and also ∠ACB = 45°
Now from right triangle ABC
tan 45° = h/x ⇒ 1 = h/x
∴ x = h
Hence, breadth of the river = height of the tower

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