Question

1. paul props a ladder against a wall which measures 10 feet. how high up on the wall will the ladder reach, if the foot of the ladder is 5 feet away from the wall?

Explanation:

Step1: Identify the triangle type

This is a right - triangle problem, with the ladder as the hypotenuse ($c = 10$ ft), the distance from the foot of the ladder to the wall as one leg ($a = 5$ ft), and the height on the wall as the other leg ($b$). We use the Pythagorean theorem: $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the formula to solve for b

We can rewrite the Pythagorean theorem to solve for $b$: $b=\sqrt{c^{2}-a^{2}}$. Substitute $c = 10$ and $a = 5$ into the formula: $b=\sqrt{10^{2}-5^{2}}=\sqrt{100 - 25}=\sqrt{75}=5\sqrt{3}\approx8.66$ (ft).

Answer:

The ladder will reach approximately $5\sqrt{3}$ feet (or about 8.66 feet) up the wall.