Question

question
if you place a 29 - foot ladder against the top of a building and the bottom of the ladder is 24 feet from the bottom of the building, how tall is the building? round to the nearest tenth of a foot.
answer attempt 1 out of 2
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Explanation:

Step1: Use Pythagorean theorem

Let the height of the building be \( h \). According to the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), where \( c = 29 \) (length of the ladder, hypotenuse) and \( a = 24 \) (distance from the bottom of the ladder to the building). So \( h^{2}+24^{2}=29^{2} \).

Step2: Solve for \( h^{2} \)

\( h^{2}=29^{2}-24^{2}=(29 + 24)(29 - 24)=(53)\times(5)=265 \).

Step3: Find \( h \)

\( h=\sqrt{265}\approx16.3 \).

Answer:

\( 16.3 \)