3. A 20 ft ladder is placed next to a building. The ladder forms a 72° angle with the ground. How far is base of the ladder from the base of the building? Round your answer to the nearest tenth of a foot. Show your work.

1. You can make a triangle as you can see in the figure attached, where [tex]x[/tex] is the distance between the base of the ladder and the base of the building

2. To solve this problem you can apply the following proccedure:

[tex]cos(\alpha)=\frac{adjacent}{hypotenuse}[/tex]

Where [tex]\alpha=72degrees\\adjacent=x\\hypotenuse=20[/tex]

3. Substitute values:

[tex]cos(72)=\frac{x}{20}\\x=(20)(cos(72))\\x=6.2[/tex]

Answer Link

alinakincsem alinakincsem · Answer 2 · 2018-10-23T12:07:28+02:00

Answer:

6.2 feet

Step-by-step explanation:

A ladder is placed next to a building which will form a right angled triangle where,

ladder = the hypotenuse,

building = perpendicular; and

distance on the ground between the building and the ladder = base

We know the hypotenuse and the angle formed between the ladder and the ground to be 72°, so we can use the formula for Cos to find the base:

Cos = Base / Hypotenuse

Supposing x to be the base:

Cos (72°) = x / 20

x = cos (72°) * 20

x = 6.2 feet

Therefore, the base is the ladder is 6.2 feet far from the base of the building.