# A flagpole casts a shadow 3.5 meters long. Anita is standing near the pole. Her shadow is 0.75 meters long. Anita's height is 1.5 meters. How tall is the flagpole?

Apr 13, 2018

$7$ metres

#### Explanation:

$0.75 : 1.5 = 3.5 : z$ ($z$ = flagpole height).

$\frac{1.5}{2} = 0.75 .$ Therefore $\frac{z}{2} = 3.5 .$

Rearrange this so $3.5 \times 2 = z$

$z = 7$

Apr 13, 2018

The flagpole is $7 m$ high.

#### Explanation:

The heights and the shadows are in the same ratio because the sun is shining from the same angle, so the triangles formed are similar.

Notice that Anita's height is twice as long as her shadow, so the height of the flagpole will be $2 \times 3.5 = 7 m$

We can also write a direct proportion:

x/3.5 = 1.5/0.75" "(larr"heights")/(larr"shadows")

$x = \frac{3.5 \times 1.5}{0.75}$

$x = 7 m$

Apr 13, 2018

Height of flagpole$= 7 m$

#### Explanation:

$\therefore \tan \theta = \frac{1.5}{0.75} = \frac{O p p o s i t e}{A \mathrm{dj} a c e n t} = 2$

$\therefore \theta = {63}^{\circ} 26 ' 5.8 ' '$

the $\angle s$ of the shadows are the same

$\therefore O p p o s i t e =$flagpole
$\therefore A \mathrm{dj} a c e n t =$length of shadow

$\therefore \frac{O p p o s i t e}{A \mathrm{dj} a c e n t} = \tan \theta = \tan {63}^{\circ} 26 ' 5.8 ' '$

$\therefore \frac{O p p o s i t e}{3.5} = 2$

flagpole$= 2 \times 3.5$

$\therefore = 7 m$