Question

A ladder leans against the side of a house. The angle of elevation of the ladder is 71° when the bottom of the ladder is 16 it from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth. X Х ? 71° 10

Answer 1

To find the length of the ladder we need to use the right triangle formed between the house, the ground, and the ladder.

We use the trigonometric function cosine, defined for an angle X as follows:

`\cos X=\frac{\text{adjacent side}}{hypotenuse}`

In this case, the known angle is:

`71`

Thus, we have to find the adjacent side to the 71° angle, and the hypotenuse of the triangle:

We will call the hypotenuse "h" just for reference.

Using the known values of the adjacent side and the angle, the cosine is:

`\cos 71=(16ft)/(h)`

The hypotenuse h is the length of the ladder, so we solve for h in the previous equation:

`h=(16ft)/(\cos 71)`

And solve the operations to find h (the length of the ladder):

`h=(16)/(0.32557)`
`h=49.14ft`

the length of the ladder is 49.14 ft.

Rounding the answer to the nearest tenth (1 decimal place):

`49.1ft`

Answer: 49.1 ft