Question

question 4 (multiple choice worth 2 points) (triangle trigonometry mc) a ladder with a length of 12 feet is leaning against a wall, with the ladders base 2 feet from the wall. how far up the wall does the ladder reach? 14 feet 12 feet 11.8 feet 4.6 feet

Explanation:

Step1: Identify the right - angled triangle

The ladder, the wall, and the ground form a right - angled triangle. The length of the ladder is the hypotenuse $c = 12$ feet and the distance of the base of the ladder from the wall is one leg $a = 2$ feet. We want to find the other leg $b$ (the height up the wall).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We can solve for $b$: $b=\sqrt{c^{2}-a^{2}}$. Substitute $c = 12$ and $a = 2$ into the formula: $b=\sqrt{12^{2}-2^{2}}=\sqrt{144 - 4}=\sqrt{140}\approx11.8$ feet.

Answer:

11.8 feet