Question

A ladder is leaned against a wall with angle of \(60^\circ\) with the ground and its foot is 6 feet away from the wall. Then the length of the ladder is:

• A. \(12\) feet
• B. \(36\) feet
• C. \(6\) feet
• D. \(24\) feet

Hint:

In right triangle problems involving angle and a side, use basic trigonometric identities: - \(\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}\) - \(\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}\) - \(\tan \theta = \frac{\text{opposite}}{\text{adjacent}}\)

Answer 1

The Correct Option is A

Step 1: Use trigonometric relation. 
We are given:
Distance from wall (adjacent side) = \(6\) ft
Angle with ground = \(60^\circ\)
We need the hypotenuse (ladder length)
From \(\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}\), \[ \cos 60^\circ = \frac{6}{\text{hypotenuse}} \Rightarrow \frac{1}{2} = \frac{6}{L} \Rightarrow L = 12 \]