Question

if a ladder leans against a house, reaching a window 5 meters high, and the base of the ladder is 3 meters from the house, what is the length of the ladder?
a. 5.83 meters
b. 4 meters
c. 6.21 meters
d. 34 meters

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 3\) (distance from house), \(b=5\) (height of window), and \(c\) is the length of the ladder.

Step2: Substitute values

Substitute \(a = 3\) and \(b = 5\) into the formula: \(3^{2}+5^{2}=c^{2}\). So, \(9 + 25=c^{2}\), which gives \(c^{2}=34\).

Step3: Solve for \(c\)

Take the square root of \(34\), \(c=\sqrt{34}\approx5.83\).

Answer:

A. 5.83 meters