3. A ladder that is 20 feet long is leaning against the side of a building. If the angle formed between the ladder and the ground is 75 degrees, how far is the bottom of the ladder from the base of the building?

Answer: Distance of bottom of the ladder from the base of the building is 5.18 feet.  Step-by-step explanation:Given:Length of ladder = 20 feet Angle formed between ladder and ground = 75 degrees.To Find:Distance of bottom of the ladder from the base of the building. Solution:   Consider the below figure forming a triangle ABC. AB is building  AC is ladder , so AC = 20 feet BC is distance between base of building and bottom of ladder. And angle between ground and ladder that is ∠C = 75degreesNeed to calculate BC ,  As triangle ABC forms right angled triangle , right angle at B , So [tex]cos C =\frac{ BC}{AC}[/tex] => BC = AC cos C => BC= 20 cos (75)=> BC = 5.18 feet Hence distance of bottom of the ladder from the base of the building is 5.18 feet.