ladders can be extremely dangerous if not used correctly. a 20 ft. extension ladder is played on a wall making and angle 85° with the ground. if a person at top of the ladder leaned back, rotating the ladder away from the wall, how far to the nearest foot would the person fall before he hit the ground?

If the person on the ladder were to lean back and fall to the ground (rotating the ladder away from the wall), then the distance he would have covered before he hits the ground is depicted by the arc as shown in the diagram. The ladder upon touching the ground would remain the same, which is 20 feet. So what the question requires is the length of the arc made during the fall, and the length of the ladder both on the wall an on the floor would be the radius (20 ft) while the angle subtended by the arc is 95° ( angles on a straight line equals 180, that is 85 + 95 = 180)

Therefore the length of an arc is given as;

Length of arc = (∅/360) x 2πr

Where ∅ = 95 and r = 95

Length of arc = (95/360) x 2 x 3.14 x 20

Length of arc = (19/72) x 125.6

Length of arc = 2386.4/72

Length of arc = 33.1444

Length of arc ≈ 33 feet (To the nearest foot)

The person on the ladder would have travelled approximately 33 feet before he/she hits the ground.

xero099 xero099 · Answer 2 · 2021-12-10T14:59:52+01:00

The person falls a distance of approximately 19.924 feet.

In this question, we must determine the vertical distance travelled by the person ([tex]y[/tex]), in feet. Let consider that the ladder is set between a horizontal ground and a vertical wall.

Then, the vertical distance is determined by the following trigonometric expression:

[tex]y = l\cdot \sin\theta[/tex] (1)

Where:

[tex]l[/tex] - Ladder length, in feet
[tex]\theta[/tex] - Ladder angle with the ground, in sexagesimal degrees

If we know that [tex]l = 20\,ft[/tex] and [tex]\theta = 85^{\circ}[/tex], then the vertical distance travalled by the person:

[tex]y = (20\,ft)\cdot \sin 85^{\circ}[/tex]

[tex]y \approx 19.924\,ft[/tex]

The person falls a distance of approximately 19.924 feet.

To learn more on trigonometric relations, we kindly invite to check this verified question: https://brainly.com/question/6904750