The angle of elevation of a ladder leaning against a wall 60° and the foot of the ladder is 12.4 m away from the wall. The length of the ladder is?
- 24.8 meters
- 6.4 meters
- 12.4 meters
- None of these
Explanation
We know:
- Angle of elevation (θ) = 60°
- Distance of the foot of the ladder from the wall (x) = 12.4 m
- We need to find the length of the ladder (hypotenuse)
Using the cosine function:
cos(θ) = adjacent side / hypotenuse
cos(60°) = 12.4 / hypotenuse
To find the hypotenuse (length of the ladder), we can rearrange the equation:
hypotenuse = 12.4 / cos(60°)
Using a calculator:
hypotenuse = 12.4 / 0.5
hypotenuse = 24.8
So, the length of the ladder is 24.8 meters.
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