A ladder is 12 ft high and has a 73 degree angel. What is the distance from the ladder to the wall

Question

A 12 foot ladder leans against a wall with a 73 degree angle.  What is the distance from the ladder to the wall

Answer 1

The first thing we do in these type of problems is to draw a diagram.  We know that in this diagram, we will have a ladder leaning against the wall.  As a result, we end up with a triangle.

 

The ladder is 12 ft high.  This is your vertical leg of the triangle.  The angle between the top of the ladder and the wall is 73 degrees.  We also know that the base of the ladder is at a distance from the wall at ground level, the horizontal leg of the triangle. This distance is what we want to find out. Since the wall is perpendicular to the ground, this forms a 90 degree angle to each other, giving us a right triangle.  This allows us to use trigonometric applications.

 

 

The length of the ladder is the hypotenuse of the triangle.  Since the hypotenuse is not known, but the one leg and an angle are known, we must use tangent function.

 

tan(73) = x / 12

 

x = the distance from the ladder to the wall

 

 

Solve for x from the tangent function.  I will let you take it from here.