Question

a 4 m ladder leans against a building. if the bottom of the ladder is 1.3 m from the bottom of the building, how far up the wall will the ladder reach?

Explanation:

Step1: Define Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c=4$ (ladder, hypotenuse), $b=1.3$ (base distance).

Step2: Rearrange for height $a$

$a = \sqrt{c^2 - b^2}$

Step3: Substitute values

$a = \sqrt{4^2 - 1.3^2} = \sqrt{16 - 1.69} = \sqrt{14.31}$

Step4: Calculate final value

$\sqrt{14.31} \approx 3.78$

Answer:

Approximately 3.78 meters