The height of a tower - Math Central

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Question from Pandey:

Hello sir plz solve this question. If the shadow of a tower is found to be 10.5m longer when the sun's altitude is 45°AND60°. Find the height of the tower.

Hi,

In my diagram below the lengths re measured in meters, so the height of the tower is $x$ meters.

tower

From the diagram you can see that

\[\tan\left( 60^2\right) = \frac{h}{x}.\]

Write an expression for $\tan(45^{o}.$

Solve the two equations for $h.$

Penny

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