Question

20 FOOT LADDER IS LEANING AGAINST A WALL THE FOOT OF THE LADDER MAKES AN ANGLE OF 58 WITH THE GROUND

Answer 1

The question is incomplete. Here is the complete question:

A 20-foot ladder is leaning against a wall. The foot of the ladder makes an angle of 58 degrees with the ground. Find, to the nearest foot, the vertical distance from the top of the ladder to the ground.

Answer:

17 ft

Explanation:

Let the height from the top of the ladder to the ground be 'x' feet.

Given:

The triangle for the given situation is shown below.

Now, from the triangle ABC, AB is the length of the ladder, A is the top of ladder, B is the foot of the ladder and AC is 'x'.

The length of the ladder is,
`AB=20\ ft`

The angle made by the foot of the ladder with the ground is,
`\angle ABC=58`°

Now, using the sine ratio for the angle ∠ABC, we have:

`\sin(\angle ABC)=(AC)/(AB)\\\sin(58)=(x)/(20)\\x=20* \sin(58)\\x=20* 0.8480\\x=16.96\approx 17\textrm{ ft (Nearest foot})`

Therefore, the vertical distance from the top of the ladder to the ground is 17 feet.