Question

to repair a roof that is 3.8 meters high, mr. dudley leans a 4.3 - 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? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Identify the problem as a right - triangle problem

We have a right - triangle where the height of the building is one leg ($a = 3.8$ meters), the length of the ladder is the hypotenuse ($c=4.3$ meters), and we need to find the other leg ($b$). We use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$.

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

$b=\sqrt{c^{2}-a^{2}}$. Substitute $a = 3.8$ and $c = 4.3$ into the formula: $b=\sqrt{4.3^{2}-3.8^{2}}$.

Step3: Calculate the values inside the square - root

First, calculate $4.3^{2}=18.49$ and $3.8^{2}=14.44$. Then $4.3^{2}-3.8^{2}=18.49 - 14.44=4.05$.

Step4: Calculate the square - root

$b=\sqrt{4.05}\approx2.0$.

Answer:

$2.0$