Question

a 12 - ft ladder is placed 5 feet from a building. approximately how high on the building does the ladder reach?
a 11 ft
b 7 ft
c 13 ft
d 14 ft

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ladder, \(c = 12\) ft) and \(a\) is the distance from the building (\(a=5\) ft). Let \(b\) be the height on the building. So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(c = 12\) and \(a = 5\) into the formula: \(b^{2}=12^{2}-5^{2}=144 - 25=119\).

Step3: Calculate \(b\)

\(b=\sqrt{119}\approx10.9\approx11\) (since \(\sqrt{121} = 11\) and \(119\) is close to \(121\)).

Answer:

A. 11 ft