Question

mike leans a 10 - foot ladder against a wall. he puts the bottom of the ladder 3 feet away from the wall. approximately how far up the wall does the ladder go? 7.0 feet 9.5 feet 10.4 feet 13.0 feet

Explanation:

Step1: Identify the problem as a right - triangle problem

The ladder, the wall, and the ground form a right - triangle. The length of the ladder is the hypotenuse $c = 10$ feet and the distance from the wall to the bottom of the ladder is one leg $a = 3$ feet. We want to find the other leg $b$ (height on the wall).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We can solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the values

Substitute $a = 3$ and $c = 10$ into the formula: $b=\sqrt{10^{2}-3^{2}}=\sqrt{100 - 9}=\sqrt{91}\approx9.5$ feet.

Answer:

B. 9.5 feet