Question

a 14 - foot ladder is set up 4 feet from the base of a building. how far up the building does the ladder reach? round your answer to the nearest tenth of a foot. 13.4 feet 14.6 feet 16.5 feet 18.0 feet

Explanation:

Step1: Apply Pythagorean theorem

Let the length of the ladder be the hypotenuse $c = 14$ feet and the distance from the base of the building to the bottom of the ladder be $a = 4$ feet. We want to find the height $b$ up the building the ladder reaches. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 4$ and $c = 14$ into the formula: $b=\sqrt{14^{2}-4^{2}}=\sqrt{196 - 16}=\sqrt{180}$.

Step3: Calculate and round

$\sqrt{180}\approx13.4$ (rounded to the nearest tenth).

Answer:

13.4 feet