How far from the house should you place the base of the ladder?

Question

The proper angle for a ladder is about 75° from the ground. Suppose you have a 8 foot ladder.

Answer 1

Like Mark says, it's a good idea to draw a diagram when you can. In this case, we can picture a ladder leaning against a wall, and we should be able to label what the values mean in the picture. In this case:

|\

| \

| \ 8 ft

| \

| \

| 75°(\

‾‾‾‾‾‾‾ X

Notice where the numbers are and what they represent. Also notice that the picture resembles a right triangle, where the angle between the wall and the ground is 90°. The hypotenuse is represented by the ladder, which we are told is 8ft, and we're also told it is at an angle 75° from the ground, hence the angle given in the picture.

Now that we have a picture that represents a right triangle, you should be able to apply the correct trigonometric function to find X, the distance of the ladder base from the house (which is just the length of the bottom side of the triangle).

As a hint, here are the possible formulas you may have to use:

sin(θ) = Opposite ÷ Hypotenuse

cos(θ) = Adjacent ÷ Hypotenuse

tan(θ) = Opposite ÷ Adjacent

We know two of the values (θ and Hypotenuse), we just have to find the value that represents X.

Answer 2

8 is the hypotenuse of a right triangle

cos75 = adjacent side divided by hypotenuse

base = adjacent side

base = 8cos75 = about 8 times .258819 = about 2.07055 feet

the base is about 2.1 feet or about 2 feet and 4/5 of an inch