Question

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

Answer 1

Completed Question

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)
`Height ,h=(x√(15))/(4) $ feet`

(d) NO

Explanation:

Part 1

Let the length of the ladder =x

Since by the given rule, Horizontal Distance =
`\frac14$ of the length of the ladder`

Horizontal Distance =
`\frac14x`

In the sketch of the problem attached below,

• The length of the ladder=AC
• Horizontal distance =BC

Part 2

From Triangle ABC

`\cos C=(BC)/(AC) \\\cos C=(x/4)/(x) \\\cos C=(1)/(4)\\ C=\arccos (1)/(4)\\C \approx 75.52^\circ`

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

`x^2=(x/4)^2+h^2\\h^2=x^2-(x^2)/(16)\\ h^2=(15x^2)/(16)\\h=\sqrt{(15x^2)/(16)} \\h=(x√(15))/(4)$ feet`

Part 4

If x=51 feet

`Height ,h=(51√(15))/(4)$ = 49.38 feet`

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