1. **Problem Statement:** A ladder makes an angle of 60° with the ground, and the foot of the ladder is 8 m away from the wall. Find the length of the ladder.
2. **Formula Used:** In a right triangle formed by the ladder, wall, and ground, the ladder is the hypotenuse, the distance from the wall is the adjacent side, and the angle with the ground is 60°. We use the cosine function:
$$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$
3. **Applying the formula:** Here, $\theta = 60^\circ$, adjacent side = 8 m, hypotenuse = length of ladder $L$.
$$\cos(60^\circ) = \frac{8}{L}$$
4. **Calculate $\cos(60^\circ)$:**
$$\cos(60^\circ) = \frac{1}{2}$$
5. **Set up the equation:**
$$\frac{1}{2} = \frac{8}{L}$$
6. **Solve for $L$:**
$$L = 8 \times 2 = 16$$
7. **Answer:** The length of the ladder is 16 m.
**Final answer: D) 16 m**
Ladder Length
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