Question

A vertical stick 30 m long casts a shadow 15 m long on the ground. At the same time, a tower casts a shadow 75 m long on the ground. The height of the tower is :

• A. 150 m
• B. 100 m
• C. 25 m
• D. 200 m

Answer 1

The correct option is A 150 m

Consider triangles ABC and EBD.
EB is a stick of length 30m, BD is the shadow of the stick measuring 15m, AB is the tower and its shadow measures 75m.
By similarity, $\frac{EB}{BD}=\frac{AB}{BC}⟹\frac{30}{15}=\frac{x+30}{75}⟹2=\frac{x+30}{75}⟹150=x+30⟹x=120$.
The height of the tower $=x+30=150m$