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, [tex]AB = x[/tex]
As per question, BC = 6.5 ft, [tex]\angle B=55[/tex]°
Using cosine ratio of the angle B, we get
[tex]\cos 55=\frac{BC}{AB}\\\\\cos 55=\frac{6.5}{x}\\\\x=\frac{6.5}{\cos 55}=11.33\textrm{ ft}[/tex]
Therefore, the length of the ladder is 11.33 ft.
