Question

to repair a roof that is 4 meters high, mr. leonard leans a 5 - meter ladder against the side of the building. to reach the roof, how far away from the building should he place the base of the ladder? meters

Explanation:

Step1: Identify the right - angled triangle

The height of the roof is one leg ($a = 4$ meters), the ladder is the hypotenuse ($c = 5$ meters), and the distance from the building to the base of the ladder is the other leg ($b$). We use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the Pythagorean theorem to solve for $b$

We get $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the values of $a$ and $c$

Substitute $a = 4$ and $c = 5$ into the formula: $b=\sqrt{5^{2}-4^{2}}=\sqrt{25 - 16}=\sqrt{9}$.

Step4: Calculate the value of $b$

$\sqrt{9}=3$.

Answer:

3