Question

HELP !!! | 20 Points.

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.

Answer 1

The ladder will not be safe.

Explanation:

The ladder is 17 ft long

The top of the ladder is 16.5 ft above the ground

The ladder makes a right triangle of height = 16.5 ft and hypotenuse = 17 ft

To find the angle the ladder makes with the ground,

Height ÷ hypotenuse = sin angle

i.e
`(16.5)/(17)` = sin angle

`sin^(-1)` angle = 76.1°

So the ladder is not safe since the angle it makes with the ground is greater than 70°.

Answer 2

No. The ladder is too steep.

Explanation:

Length of ladder = 17 feet. This is the hypotenuse.

Side a of a right triangle = 16.6

To answer this, you need one of the trigonometric functions.

Opposite = 16.5

hypotenuse = 17

The function you need is the sine function.

Sin(theta) = opposite / hypotenuse

sin(theta) = 16.5 / 17

Sin(theta) = 0.97059

theta = sin-1(0.07059)

theta = 76.07

No the ladder is too steep.