Question

a 10-foot-tall ladder is placed against a wall so that the top of the ladder is 9 feet above the ground. how far is the base of the ladder from the base of the wall along the ground, to the nearest tenth? (just type the number of feet in the answer box.)

Explanation:

Step1: Identify the triangle type

This is a right triangle with hypotenuse (ladder) \( c = 10 \) and one leg (height on wall) \( a = 9 \). We need to find the other leg \( b \) (distance from base to wall).

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 \( c = 10 \) and \( a = 9 \): \( b=\sqrt{10^{2}-9^{2}}=\sqrt{100 - 81}=\sqrt{19}\approx4.4 \) (rounded to the nearest tenth).

Answer:

4.4