Question

The length, breadth and height of a room are 10 m, 10√2 m and 10 m respectively. The angle of elevation of a top corner of room from any point on a diagonal of the base of the room is

• A. 45°
• B. 60°
• C. 30°
• D. None

Answer 1

The Correct Option is C

Given, the length of the room \(L = 10\) m, breadth \(B = 10\sqrt{2}\) m, and height \(H = 10\) m.
The diagonal of the base of the room can be calculated using the Pythagoras theorem: \[ \text{Diagonal of base} = \sqrt{L^2 + B^2} = \sqrt{10^2 + (10\sqrt{2})^2} = \sqrt{100 + 200} = \sqrt{300} = 10\sqrt{3} \text{ m} \] Now, to find the angle of elevation \(\theta\), we consider the right triangle formed by the diagonal of the base, the height of the room, and the line of sight to the top corner. The angle of elevation is given by: \[ \tan \theta = \frac{H}{\text{Diagonal of base}} = \frac{10}{10\sqrt{3}} = \frac{1}{\sqrt{3}} \] Therefore, \[ \theta = 30^\circ \]

The correct option is (C): \(30°\)