The angle of elevation of a ladder leaning against a wall is 60deg and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

To solve this problem, we can use the properties of a right triangle and the trigonometric function called cosine.

The cosine of an angle in a right triangle is defined as the adjacent side divided by the hypotenuse. In this case, the adjacent side is the distance from the wall to the foot of the ladder (4.6 m), and the hypotenuse is the length of the ladder, which we are trying to find.

So, we can set up the equation as follows:

cos(60) = 4.6 / length of the ladder

We know that cos(60) = 0.5, so we can substitute that into the equation:

0.5 = 4.6 / length of the ladder

To solve for the length of the ladder, we can multiply both sides of the equation by the length of the ladder and then divide both sides by 0.5:

length of the ladder = 4.6 / 0.5

length of the ladder = 9.2 m

So, the length of the ladder is 9.2 meters.