A 13ft ladder is leaning against a building with a the base of the ladder leaning 2ft away from the building.

Question

How high will it reach?

Answer 1

Assuming that the ground is horizontal and the building wall is vertical we have a right triangle and can use Pythagoras' Theorem.

       Let H be the height where the ladder touches the building.

         H^2 + 2^2 = 13^2

             H^2 = 165           (subtract 4 from both sides)

              H = ±12.84   

      Height is 12 ft 10 inches           (choose +; also, sorry, no one uses tenth of a foot rulers) 

Answer 2

A picture would be helpful, so I'll try to paint one with words.  Imagine the ladder as the hypotenuse of a right triangle.  The side of the building, from where the ladder touches it to the ground, is one leg of the triangle (let's call this Leg1).  The ground, from where the ladder touches it to the side of the building, is the other leg (Leg2).  We are trying to solve for the length of Leg1.

 

We can use the Pythagorean Theorem,

A^2 + B^2 = C^2, or (Leg1)^2 + (Leg2)^2 = (hypotenuse)^2.

 

We already have Leg2 = 2 ft, and hypotenuse = 13 ft.

Let's plug these values into the equation, and solve for the missing leg.

Leg1^2 + 2^2 = 13^2

Leg1^2 + 4 = 169

Leg1^2 = 165

Leg1 = √165.

 

The prime factorization of 140 is 3*5*11, so we can't pull any numbers out of the square root.

Leg1 = √165, which to 2 decimal places comes out to 12.85 ft

 

(edited to fix an error)