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

Answer:

11.33 feet

Step-by-step 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

$\cos 55=\frac{BC}{AB}\\\\\cos 55=\frac{6.5}{x}\\\\x=\frac{6.5}{\cos 55}=11.33\textrm{ ft}$

Therefore, the length of the ladder is 11.33 ft.