Question

If a vertical stick $12\text{m}$ long casts a shadow $8\text{m}$ long on the ground and at the same time a tower casts a shadow $40\text{m}$ long on the ground, then the height of the tower is

• A. $40\text{m}$
• B. $50\text{m}$
• C. $75\text{m}$
• D. $60\text{m}$

Answer 1

The correct option is D $60\text{m}$

Let the height of the tower be $x$ metres

Since the two triangles are similar by AA similarity criterion, we have

$\frac{x}{40}=\frac{12}{8}$

$\Rightarrow x=\frac{12}{8}\times 40=12\times 5=60\text{m}$

Hence, height of tower is $60\text{m}$.