Question

A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is 45⁰. Then which of the following statements is correct?

• A. The breadth of the river is half of the height of the tower.
• B. The breadth of the river and the height of the tower are the same.
• C. The breadth of the river is twice the height of the tower.
• D. None of these

Answer 1

The Correct Option is B

\(\tan = \frac{perpendicular}{base}\)

So, in right angled triangle,

\(\tan 45\degree = \frac{\text{height of tower}}{\text{breadth of river}}\)

Since \(\tan 45\degree = 1\)

\(\therefore\) \(\text{height of tower = breadth of river}\)

Hence, the correct option is (B): The breadth of the river and the height of the tower are the same