The shadow of a tower increases by 20 m when the sun's altitude changes from 60\(^\circ\) to 45\(^\circ\). Find the length (rounded off to one decimal place, in m) of the tower. (Use \(\sqrt3 = 1.7\))
48.6
Let the tower's height be h. Shadow at 60°: \(\dfrac{h}{\sqrt3}\). Shadow at 45°: \(h\).
Difference: \(h - \dfrac{h}{\sqrt3} = 20\).
Using \(\sqrt3=1.7\): \(h\left(1-\dfrac{1}{1.7}\right) = h\times0.4118 = 20 \Rightarrow h \approx 48.6\).
Hence, the length of the tower is approximately 48.6 m.
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