Question

a 10 - ft ladder leans against the side of a house. the bottom of the ladder is 5 ft from the side of the house. how high is the top of the ladder from the ground? if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the height be \( h \). According to \( a^{2}+b^{2}=c^{2} \), here \( c = 10\) (ladder length, hypotenuse), \( a = 5\) (distance from house), and \( b=h \). So \( h^{2}+5^{2}=10^{2} \).

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

\( h^{2}=10^{2}-5^{2}=100 - 25=75 \).

Step3: Find \( h \)

\( h=\sqrt{75}\approx8.7 \) (rounded to the nearest tenth).

Answer:

\( 8.7 \)