A ladder 3

A 30 foot ladder is set against the side of a house so that it reaches up 24 feet. If Elizabeth grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? Round to the nearest tenth of a foot.

Final Answer:

h₂ =  21.4 ft

Step-by-step explanation:

$$\begin{gathered} c=30\text{ft} \\ {h}_1=24\text{ft} \\ {c}^2=h_1^2+a_1^2 \\ {a}_1=\sqrt{c^2-h_1^2}=\sqrt{30^2-24^2}=18\text{ft} \\ {a}_2=a_1+3=18+3=21\text{ft} \\ {h}_2=\sqrt{c^2-a_2^2}=\sqrt{30^2-21^2}=3\sqrt{51}=21.4\text{ft} \end{gathered}$$

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