Question

suppose a ladder is leaned up against a wall with an angle of elevation, \\(\theta\\) as shown above. if we want the bottom of the ladder to be placed a distance from the wall that is half the ladders length, which of these angles should be used?

1.503 radians
1.161 radians
1.047 radians
0.524 radians

Explanation:

Set up the trigonometric ratio

Using the Trigonometric Ratios knowledge point

$$ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{\frac{L}{2}}{L} = \frac{1}{2} $$

Solve for the angle in radians

We need to find the angle \(\theta\) in radians such that \(\cos(\theta) = 0.5\).

$$ \theta = \arccos(0.5) = \frac{\pi}{3} \approx 1.047197\text{ radians} $$

Match with the given options

Comparing the calculated value to the choices:

$$ \theta \approx 1.047\text{ radians} $$

Answer:

• 1.503 radians
• 1.161 radians
• 1.047 radians (Correct answer)
• 0.524 radians