1. OSHA is an agency responsible for workplace safety, read its rule and sketch a diagram that shows the proper relationship between the ladder, wall and ground

1. OSHA is an agency responsible for workplace safety, read its rule and sketch a diagram that shows the proper relationship between the ladder, wall and ground .

Rule: Non-self-supporting ladders, which must lean against a wall or other support, are to be positioned at such an angle that the horizontal distance from the top support to the foot of the ladder is about the 1/4 working length of the ladder.

2. Calculate the angle that the ladder makes with the ground using a trigonometric ratio.

3. If a ladder is x feet long, how high up a wall can it safely reach?

4. Would a 51-foot ladder be long enough to climb a 50-foot wall?

Answer:

(a)See attachment

(b)75.52 degrees

(c)[tex]Height ,h=\dfrac{x\sqrt{15}}{4} $ feet[/tex]

(d) NO

Step-by-step explanation:

Part 1

Let the length of the ladder =x

Since by the given rule, Horizontal Distance =[tex]\dfrac14$ of the length of the ladder[/tex]

Horizontal Distance = [tex]\dfrac14x[/tex]

In the sketch of the problem attached below,

The length of the ladder=AC
Horizontal distance =BC

Part 2

From Triangle ABC

[tex]\cos C=\dfrac{BC}{AC} \\\cos C=\dfrac{x/4}{x} \\\cos C=\dfrac{1}{4}\\ C=\arccos \dfrac{1}{4}\\C \approx 75.52^\circ[/tex]

The angle that the ladder makes with the ground is 75.52 degrees.

Part 3

If the ladder is x feet long

Using Pythagoras theorem in Triangle ABC below

[tex]x^2=(x/4)^2+h^2\\h^2=x^2-\dfrac{x^2}{16}\\ h^2=\dfrac{15x^2}{16}\\h=\sqrt{\dfrac{15x^2}{16}} \\h=\dfrac{x\sqrt{15}}{4}$ feet[/tex]

Part 4

If x=51 feet

[tex]Height ,h=\dfrac{51\sqrt{15}}{4}$ = 49.38 feet[/tex]

Therefore, a 51 feet ladder would not be enough to climb a 50 feet wall as it would violate the safety rule.