Question

1. a 6 - ft ladder is placed against a wall with its base 2.5 ft from the wall. how high above the ground is the top of the ladder?

Explanation:

Step1: Recognize right - triangle

The ladder, wall, and ground form a right - triangle. The length of the ladder is the hypotenuse $c = 6$ ft and the distance from the base of the ladder to the wall is one leg $a = 2.5$ ft. We want to find the other leg $b$.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Rearranging for $b$, we get $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 2.5$ and $c = 6$ into the formula: $b=\sqrt{6^{2}-2.5^{2}}=\sqrt{36 - 6.25}=\sqrt{29.75}$.

Step3: Calculate the value

$\sqrt{29.75}\approx5.45$ ft.

Answer:

$5.45$ ft