2-meter-long 81619

How tall is the tree if I lean a 2-meter-long ladder against it? The ladder is 0.7 m away from the tree, and the top of the ladder rests against the tree at 2/3 of its height.

Correct answer:

x =  2.8102 m

Step-by-step explanation:

$$\begin{gathered} c=2\text{m} \\ a=0.7\text{m} \\ {a}^2+b^2=c^2 \\ b=\sqrt{c^2-a^2}=\sqrt{2^2-0.7^2}\doteq 1.8735\text{m} \\ b=2/3x \\ x=\frac{3}{2}\cdot b=\frac{3}{2}\cdot 1.8735=2.8102\text{m} \end{gathered}$$

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