Question

a ladder leans against a wall: 6 ft from the wall and 14 ft high on the wall. ladder length? 15.3 feet 13 feet 15.2 feet 12.6 feet

Explanation:

Step1: Identify the problem type

This is a right - triangle problem where the ladder forms the hypotenuse, the distance from the wall is one leg ($a = 6$ ft), and the height on the wall is the other leg ($b=14$ ft). We use the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $c$ is the length of the ladder.

Step2: Substitute the values into the formula

First, calculate $a^{2}$ and $b^{2}$. $a^{2}=6^{2} = 36$, $b^{2}=14^{2}=196$. Then, find the sum: $a^{2}+b^{2}=36 + 196=232$.

Step3: Calculate the square root

Now, find $c=\sqrt{232}$. $\sqrt{232}=\sqrt{4\times58}=2\sqrt{58}\approx2\times7.62 = 15.24\approx15.2$ (or more accurately, $\sqrt{232}\approx15.23$ which is close to 15.2 feet).

Answer:

15.2 feet (the option with the diamond symbol: 15.2 feet)