Question

the formula that relates the length of a ladder, ( l ), that leans against a wall with distance ( d ) from the base of the wall and the height ( h ) that the ladder reaches up the wall is ( l = sqrt{d^2 + h^2} ). what height on the wall will a 15 - foot ladder reach if it is placed 3.5 feet from the base of a wall?
13.1 feet
11.5 feet
14.6 feet
15.4 feet

Explanation:

Step1: Rearrange the formula for \( h \)

Given \( L = \sqrt{d^2 + h^2} \), square both sides: \( L^2 = d^2 + h^2 \). Then, solve for \( h \): \( h = \sqrt{L^2 - d^2} \).

Step2: Substitute \( L = 15 \) and \( d = 3.5 \)

Calculate \( L^2 = 15^2 = 225 \) and \( d^2 = 3.5^2 = 12.25 \). Then, \( L^2 - d^2 = 225 - 12.25 = 212.75 \).

Step3: Find \( h \)

Take the square root: \( h = \sqrt{212.75} \approx 14.6 \).

Answer:

14.6 feet