A 13-m-long ladder reaches a window of a building 12m above the ground. Determine the distance of the foot of the ladder from the building.
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Let AB be the building and CB be the ladder. Then, $\text{AB}=12\text{m},\text{CB}=13\text{m}$ and $\angle\text{CAB}=90^\circ$
By Pythagoaras theoram, we have $\text{CB}^2=\text{AB}^2+\text{AC}^2$ $\text{AC}^2=\big[\text{CB}^2-\text{AB}^2\big]$ $=\Big[(13)^2-(12)^2\Big]\text{m}^2$ $=(169-144)\text{m}^2$ $=25\text{m}^2$ $\Rightarrow\text{AC}=\sqrt{25}\text{m}=5\text{m}$ Hence, the distance of the fool of the ladder from the building is 5m.
By Pythagoaras theoram, we have $\text{CB}^2=\text{AB}^2+\text{AC}^2$ $\text{AC}^2=\big[\text{CB}^2-\text{AB}^2\big]$ $=\Big[(13)^2-(12)^2\Big]\text{m}^2$ $=(169-144)\text{m}^2$ $=25\text{m}^2$ $\Rightarrow\text{AC}=\sqrt{25}\text{m}=5\text{m}$ Hence, the distance of the fool of the ladder from the building is 5m.
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