# Can someone plz help me?

Mar 27, 2018

25 ft

#### Explanation:

The triangles are proportional. There is the small triangle (5 ft, 6 ft, hypotenuse). There is the larger triangle that includes the small triangle (30 ft, height).

That means the side lengths are proportional.

$\frac{5}{h} = \frac{6}{30 + 6} \rightarrow$ The side lengths of the small triangle over the side lengths of the large triangle, with $h$ representing the unknown height.

Now, let's solve the proportion:

$\frac{5}{h} = \frac{6}{30} \rightarrow$ Simplify the second fraction

$\frac{5}{h} = \frac{1}{5} \rightarrow$ Cross multiply (multiply the h by 1, the 5 by 6) and set the products equal to each other

$h = 5 \cdot 5$

$h = 25 \rightarrow$ This is the height

Mar 27, 2018

The height of the statue ($h$) is $25$ feet.

#### Explanation:

Since the smaller triangle and the larger triangle are similar, we can set up a proportion between them.

Sometimes it is easier to say it out loud in English first:

$\text{The ratio of the distance from the right point to the person (6 ft.) and the person's height (5 ft.)}$

$\text{is proportional to}$

$\text{the ratio of the distance from the right point to the statue (30 ft.) and the statue's height (h ft.).}$

Now write down that proportion in math and solve for $h$:

$\left(6 \text{ ft")/(5" ft")=(30" ft")/(h" ft}\right)$

$\left(6 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{ft")/(5color(red)cancelcolor(black)"ft")=(30color(red)cancelcolor(black)"ft")/(hcolor(red)cancelcolor(black)"ft}}}}\right)$

$\frac{6}{5} = \frac{30}{h}$

$6 h = 30 \cdot 5$

$6 h = 150$

$h = \frac{150}{6}$

$h = 25$

That's the answer. Hope this helped!

Mar 27, 2018

$H = 25 f t$

#### Explanation:

assume the height of the statue is h and set a proportion:
(height of the man / length of his shadow) = (height of the statue/ length of its shadow)
$\frac{5 f t}{6 f t} = \frac{h}{30 f t}$
then cross multiply
30ft $\cdot$5ft = h ft $\cdot$ 6ft
so, $150 f t = 6 h f t$
$H = \left(\frac{150}{6}\right) f t$
$H = 25 f t$