Question

A telephone pole cast a shadow that is 37 m long find the height of the telephone pole if a statue that is 33 cm tall cast a shadow 83 cm long ?

Answer 1

By similar triangles we know:

h1/x1=h2/x2

p/37=33/83 multiply both sides by 37

p=1221/83 m

p≈14.71 m (to nearest hundredth of a centimeter)

Answer 2

The height of the telephone pole is 14.711 m (Approx) .

Explanation:

Let us assume that the height be x .

Let us assume that the shadow be y .

(As the shadow is always proportional to the height .)

Thus

`x\propto y`

y = kx

Where k is the constant of proportionality .

As given

if a statue that is 33 cm tall cast a shadow 83 cm long .

y = 83 cm

x = 33 cm

Put in the equation y = kx .

83 = 33k

`k = (83)/(33)`

As given

A telephone pole cast a shadow that is 37 m .

Let us assume that the height of the telephone pole be z .

As

1m = 100cm

37m = 3700 cm

y = 3700 cm

x = z

Put in the equation y = kx .

3700 = zk

`k = (3700)/(z)`

Compare the value of k .

`(3700)/(z) = (83)/(33)`

`(3700* 33)/(83) =z`

`(122100)/(83) =z`

z = 1471.1 cm(Approx)

As

`1\ cm = (1)/(100)\ m`

`1471.1\ cm = (1471.1)/(100)\ m`

= 14.711 m (Approx)

Therefore the height of the telephone pole is 14.711 m (Approx) .