question_answer

A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time (a) the length of the shadow cast by another pole 10 m 50 m high (b) the height of a pole which cast a shadow 5 m long.

Answer:

(a) Let the length of the shadow be x m.

Height 5 m 60 cm 10 m 50 cm Length 3 m 20 cm x 5 m 60 cm = 5.60 m

3 m 20 cm = 3.20 m

10 m 50 cm = 10.50 m

\[\therefore \]                        \[\frac{5.60}{3.20}=\frac{10.50}{x}\]

\[\Rightarrow \]         \[x=\frac{10.50\times 3.20}{5.60}\]

\[\Rightarrow \]           x = 6m

(b) Let the height of a pole be y m.

Height (m) 5.60 cm y Length (m) 3.20 cm 5 \[\frac{5.60}{3.20}=\frac{y}{5}\]

\[\Rightarrow \,\,\,y=\frac{5.60\times 5}{3.20}=8.75\]

or                y = 8 m 75 cm