Question

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 1

The length of the latter would be 23 feet because we know one angle is 75 and the angle against the wall is 90 and the base is 6 feet answer is 23 feet

Answer 2

Answer:

$23.18 ft$

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$cos\theta=\frac{adjacentSide}{hypotenuse}=\frac{a}{h}$

Where $\theta$ is the angle, in this case is equal to: $\theta =75$.

$a$ is the adjacent side to the angle of 75: $a=6$, and $h$ is the hypotenuse of the triangle that is the length of the ladder, so in the last equation we clear for $h$

$h=\frac{a}{cos\theta}$

and substituting known values:

$h=\frac{6}{cos(75)}$

$h=\frac{6}{0.2588}$

$h=23.18 ft$

The length of the ladder is $23.18 ft$