Question

A Minar A casts a shadow 150 m long at the same time when a Minar B casts a shadow 120 m long on the ground. If the height of the Minar B is 80 m, find the length of Minar A.

Answer 1

Let $AB\mathrm{and}DE$ be the Minar $A$ and Minar $B$, respectively. Let $BC$ and $EF$ be the shadows of Minar $A$ and Minar $B$.
Thus, we have:
$BC=150$ m, $EF=120$ m and $DE=80$ m
Let $AB=h$ and $\theta$ be the angle of elevation of both Minars.

From ∆$DEF$, we have:
$\tan \theta =\frac{DE}{EF}=\frac{80}{120}=\frac{2}{3}$

From ∆$ABC$, we have:
$\tan \theta =\frac{AB}{BC}=\frac{h}{150}$

⇒$\frac{2}{3}=\frac{h}{150}$ [ $\tan \theta =\frac{2}{3}$]

⇒ $h=\frac{150\times 2}{3}=100$ m
∴ Length of Minar $A$ = $AB=h=100$ m