A ladder is leaning against a wall and makes an angle of 60° with the ground. If the length of the ladder is 24 m, find the distance of the foot of the ladder from the wall.
12 m
To find the distance of the foot of the ladder from the wall, we can use the concept of trigonometry. In this scenario, we have a right-angled triangle where:
- The ladder serves as the hypotenuse (with a length of 24 m).
- The angle between the ladder and the ground is given as 60°.
- We need to find the adjacent side, which is the distance of the foot of the ladder from the wall.
We use the cosine function since it relates the adjacent side and the hypotenuse:
\(\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}\)
Here, \(\theta = 60^\circ\). Therefore,
\(\cos(60^\circ) = \frac{\text{Adjacent}}{24}\)
Since \(\cos(60^\circ) = \frac{1}{2}\), we have:
\(\frac{1}{2} = \frac{\text{Adjacent}}{24}\)
To find the value of the adjacent side, we multiply both sides by 24:
\(\text{Adjacent} = 24 \times \frac{1}{2} = 12 \text{ m}\)
Thus, the distance of the foot of the ladder from the wall is 12 m.
The correct answer is 12 m.
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