Question

A $5$ m $60$ cm high vertical pole casts a shadow $3$ m $20$ cm long. Find the height of a pole which casts a shadow $5$ m long at the same time.

• A. $8$ m $75$ cm
• B. $9$ m
• C. $5$ m $25$ cm
• D. $4$ m

Answer 1

Answer: (A)

$8$ m $75$ cm

Let the first vertical pole be denoted by $AB$ and its shadow be denoted by $BC$.

Given height of first vertical pole $AB=5$ m $60$ cm $=5.6$ m and length of its shadow $BC=3$ m $20$ cm = $3.2$ m.

The second pole is denoted by $PQ$ and its shadow be denoted by $QR$.

Let $PQ=h$ m. Length of its shadow $QR=5$ m.

We need to find the height of the second pole at the same time. Hence the angle of depression in both cases is the same and let it be denoted by $\theta$.

From figure 1 (pole $AB$ ),

$tan\theta =\frac{A^{\prime }C}{A{A}^{\prime }}=\frac{AB}{BC}=\frac{5.6}{3.2}$ ---------------(1)

From figure 2 (pole $PQ$)

$tan\theta =\frac{P^{\prime }R}{P{P}^{\prime }}=\frac{PQ}{QR}=\frac{h}{5}$ -----------------(2)

Equating (1) and (2)

$\frac{5.6}{3.2}=\frac{h}{5}$

$h=\frac{5.6\times 5}{3.2}=8.75$m $=8$m $75$cm.

Therefore , height of second pole is $8$m $75$cm.