Question

Find the height of a tower whose shadow is 10 m long when the sun's altitude is 45°.

Answer 1

Let $AB$ be the tower such that $AB=h$ m and $BC$ be its shadow such that $BC=10$ m and ∠$ACB={45}^{\mathrm{o}}$.

From ∆$ABC$, we have:
$\frac{AB}{BC}=\tan {45}^{\mathrm{o}}=1$
⇒ $\frac{h}{10}=1$
⇒ $h=10$ m

Hence, the height of the tower is 10 m.