Question

if you place a 39-foot ladder against the top of a 34-foot building, how many feet will the bottom of the ladder be from the bottom of the building? round to the nearest tenth of a foot.
answer attempt 1 out of 2
ft

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the ladder is the hypotenuse ($c = 39$ ft), the building height is one leg ($a = 34$ ft), and we need to find the other leg ($b$) (distance from ladder bottom to building bottom). We use the Pythagorean theorem: $a^2 + b^2 = c^2$.

Step2: Rearrange the formula to solve for \( b \)

Rearrange the Pythagorean theorem: $b^2 = c^2 - a^2$. Substitute $c = 39$ and $a = 34$: $b^2 = 39^2 - 34^2$.

Step3: Calculate the squares

Calculate $39^2 = 1521$ and $34^2 = 1156$. Then $b^2 = 1521 - 1156 = 365$.

Step4: Take the square root and round

Take the square root of 365: $b = \sqrt{365} \approx 19.1$ (rounded to the nearest tenth).

Answer:

19.1