If the length of the ladder placed against a wall is twice the distance between the foot of the ladder and the wall. Find the angle made by the ladder with the horizontal.

Given that, 

Length of the ladder placed against a wall is twice the distance between the foot of the ladder and the wall.  

Now we have to find the angle made by the ladder with the horizontal 

From the figure, 

Distance between foot of the ladder and the wall is $B C = x$

Length of the ladder $AC= 2x$

The angle made by the ladder with the horizontal is ∠ACB

$$\Rightarrow cos 𝜃 = \frac{Adjacent side}{Hypotenuse}$$

$\Rightarrow 𝑐𝑜𝑠 \theta = \frac{x}{2x}$

$\Rightarrow 𝑐𝑜𝑠 \theta = \frac{1 }{2}$

$\Rightarrow \cos 𝜃= \cos 60°$

 $$\Rightarrow 𝜃 =60°$$

$$\Rightarrow \angle ACB=60°$$

Hence,angle made by the ladder with the horizontal is

60°