Aladder 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

To solve the problem we must know the concept of trigonometric functions. The length of the ladder is 23.1822 ft.

The basic trignometric fuctions are,

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Given to us

The angle made by the ladder with the ground, θ = 75°

The foot of the ladder is 6 feet from the base of the wall.

As we know that the length between the ladder is 6 feet from the base of the wall, therefore, it is the base of the triangle, while the ladder makes 75° with the ground.

Substitute the values of the trigonometric function of Cos,

Hence, the length of the ladder is 23.1822 ft.

Learn more about Trigonometric functions:

link

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

Where is the angle, in this case is equal to: .

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

and substituting known values:

The length of the ladder is

szdxfcgvhbjn

step-by-step explanation:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11