Question

a 14 - foot ladder is leaning against a building, with the base of the ladder 5 feet from the building. how high up on the building will the top of the ladder reach? the ladder will reach ft high up on the building. (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply Pythagorean theorem

Let \( h \) be the height. By \( a^{2}+b^{2}=c^{2} \), here \( c = 14 \), \( a = 5 \), \( b=h \). So \( 5^{2}+h^{2}=14^{2} \).

Step2: Solve for \( h \)

\( h^{2}=14^{2}-5^{2}=196 - 25=171 \). Then \( h=\sqrt{171}=\sqrt{9\times19}=3\sqrt{19} \).

Answer:

\( 3\sqrt{19} \)