Question

A 9 m ladder rests against the side of a wall. The bottom of the ladder is 1.5 m from the base of the

wall. Determine the measure of the angle between the ladder and the ground, to the nearest degree.

1 degree


80 degrees


53 degrees


10 degrees

Answer 1

9514 1404 393

Answer:

(b) 80°

Explanation:

The relevant trig relation is ...

Cos = Adjacent/Hypotenuse

The 1.5 meter distance to the wall is the side adjacent to the angle with the ground. The 9 m length of the ladder is the hypotenuse of the triangle modeling this situation.

cos(angle) = 1.5/9 = 1/6

angle = arccos(1/6) ≈ 80.4°

The angle between the ladder and the ground is about 80°.

_____

Additional comment

The Ladder Association recommends an angle of 75° for safety. At 80°, the ladder may have a tendency to tip the user backward.