A 12-foot ladder is leaning against a wall. The distance from the base of the wall to the base of the ladder is feet. Given this information, what can be determined about the triangle formed by the ground, wall, and ladder? Check all that apply.

Accepted Solution

Putting into diagram the information provided. The triangle formed is a right triangle. (Find Attached).

We are given the length of the ladder and the distance of the base of the ladder from the wall. With that we can solve for the height of the triangle as well as the angle of inclination wrt to the floor and foot of the ladder or the wall to the tip of the ladder.

Pythagorean's theorem provides for the following formula

Square of hypotenuse (longest side of the triangle) equals the sum of the squares of the two other sides for right triangles.

Length of ladder being the hypotenuse we have below equation
Hypotenuse = 12
Distance from the base to the foot of ladder = 1 foot/feet
height = ?

12² = 1² + h²
h = √144-1

Solving for inclination with respect to wall to tip of the ladder we can use rule of sine for right triangle

sineФ = opposite side / hypotenuse
sineФ = 1/12 = 0.083333
Ф = sin^-1 or inverse sine of 0.083333
Ф = 4.78017268 degrees

Note : If the distance between the base is not interpreted correctly, just change the value and plugin to the equation to get the result.