Question

a 12 - foot ladder rests against the side of a house. the base of the ladder is 3 feet away from the side of the house. how high above the ground is the top of the ladder? round to the nearest tenth of a foot. a. 9.1 feet b. 11.6 feet c. 12.4 feet d. 153.0 feet please select the best answer from the choices provided

Explanation:

Step1: Identify right triangle sides

Ladder = hypotenuse $c=12$ ft, base $a=3$ ft, height $b=?$

Step2: Apply Pythagorean theorem

$$a^2 + b^2 = c^2$$
Rearrange to solve for $b$:
$$b = \sqrt{c^2 - a^2}$$

Step3: Substitute values and calculate

$$b = \sqrt{12^2 - 3^2} = \sqrt{144 - 9} = \sqrt{135}$$

Step4: Compute and round result

$\sqrt{135} \approx 11.6$ feet

Answer:

B. 11.6 feet