Question

1. Joshua has a ladder that is 17 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. Will the ladder be safe at this height? Show your work please.

Help please???

Answer 1

The question is asking to solve a problem that'll "add up", or in other words, makes sense; through the use of Trigonometric functions. The leaning ladder is the hypotenuse of 17ft, adjacent to that is a wall that measures 16.5ft above the ground. The angle both sides make must be <=70°. The function here is Opposite over Hypotenuse i.e 16.5/17 . We use the inverse operation of Sin which is Sin^(-1) to find if the angle is < or = to 70°. Using a calculator, we find the angle to be 76.06°, which is > more than, 70°.

Thus, the ladder will not be safe for its height and therefore won't make sense.

Answer 2

No

Explanation:

It is given that Joshua has a ladder that is 17 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5 ft above the ground. Thus,

Use Sine function , we have

`\sin(angle)=\frac{\text{Height}}{\text{Ladder length}}`

`\text{Height}=\text{ladder length}{*}\sin(angle)`

Substituting the given values, we have

Height represents the height of wall.

`\text{Height}=17\sin70^(\circ)`

`\text{Height}=17(0.939)`

`\text{Height}=15.98\text{ ft}`

So the ladder will only reach maximum height of 15.98 ft , just short of 0.52 ft. at the maximum angle of 70 degrees.

Hence, The ladder will not be safe for 16.5 ft height of wall.