a ladder leaning against a wall makes an angle of 75 with the ground. If the foot of the ladder is 6 feet from the base of the wall, what is the length of the ladder

Answer:[tex]23.18 ft[/tex]Step-by-step explanation:To solve this problem, we make use of the geometry that forms between the wall, the floor and the ladder. A rectangular triangle is formed due to the right angle on the wall, see attached image.We use the cosine function[tex]cos\theta=\frac{adjacentSide}{hypotenuse}=\frac{a}{h}[/tex]Where [tex]\theta[/tex] is the angle, in this case is equal to: [tex]\theta =75[/tex].[tex]a[/tex] is the adjacent side to the angle of 75: [tex]a=6[/tex], and [tex]h[/tex] is the hypotenuse of the triangle that is the length of the ladder, so in the last equation we clear for [tex]h[/tex][tex]h=\frac{a}{cos\theta}[/tex]and substituting known values:[tex]h=\frac{6}{cos(75)}[/tex][tex]h=\frac{6}{0.2588}[/tex][tex]h=23.18 ft[/tex]The length of the ladder is [tex]23.18 ft[/tex]