A ladder leans against a vertical wall. The angle whose cosine is 0.6 with the ground. The distance between the foot of the ladder and the base of the wall is 1.2 m. Cal be lengn of the ladder.

This problem involves trigonometry, specifically the cosine function, in the context of a right-angled triangle formed by the ladder, the wall, and the ground.

Step 1: Identify the given information and the relationship. Let $L$ be the length of the ladder (hypotenuse). Let $D$ be the distance between the foot of the ladder and the base of the wall (adjacent side). Let $\theta$ be the angle the ladder makes with the ground. We are given:

• $\cos(\theta) = 0.6$
• $D = 1.2 \text{ m}$

The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step 2: Substitute the known values into the formula. $\cos(\theta) = \frac{D}{L}$ $0.6 = \frac{1.2 \text{ m}}{L}$

Step 3: Solve for $L$. To find $L$, rearrange the equation: $L = \frac{1.2 \text{ m}}{0.6}$ $L = 2 \text{ m}$

The length of the ladder is $\boxed{\text{2 m}}$.