A staircase with a length of 13 m is attached to the wall of the house. To what height is the upper

A staircase with a length of 13 m is attached to the wall of the house. To what height is the upper end of the staircase raised if the lower end is 5 m from the wall?

If we connect the points of the ends of the stairs with the bottom point of the house, we get a right-angled triangle with a leg equal to 5 m and a hypotenuse equal to 13 m.Let’s find the unknown leg according to the Pythagorean theorem (the sum of the squares of the legs in a right-angled triangle is equal to the square of the hypotenuse):

a² + b² = c²;

a² + 5² = 13²;

a² + 25 = 169;

a² = 169 – 25;

a² = 144;

a = √144;

a = 12 m – (unknown leg = height) the upper end of the ladder is raised to this height.

Answer: 12 m