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.

6.2 feet.

Step-by-step explanation:

1. You can make a triangle as you can see in the figure attached, where 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:

Where

3. Substitute values:

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.

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2