Question

A ladder leaning against a wall makes an angle of 55 pour-cent with the ground. If the foot of the ladder is 6.5 feet from the wall ,what is the length of the ladder to the nearest hundredth?

Answer 1

11.33 feet

Explanation:

The triangle for the given scenario is drawn below.

From the triangle ΔABC, AB is the length of the ladder, B is the foot of the ladder, AC is the wall, BC is the distance of the foot from the wall, and angle B is the angle of elevation of the ladder with ground.

Let the length of the ladder,
`AB = x`

As per question, BC = 6.5 ft,
`\angle B=55`°

Using cosine ratio of the angle B, we get

`\cos 55=(BC)/(AB)\\\\\cos 55=(6.5)/(x)\\\\x=(6.5)/(\cos 55)=11.33\textrm{ ft}`

Therefore, the length of the ladder is 11.33 ft.