Question

Need answer ASAP!!!!! This is a picture of the Ilanaaq Inukshuk, a monument to the 2010 Winter Olympics in Vancouver, British Columbia. An inukshuk is a landmark made of stones balanced to look like a person, used by the indigenous Inuit in Canada.
How can the people in this photograph use similar triangles to estimate the height of this inukshuk?

Answer 1

Answer:

If we measure the shadow of the monument and the shadow of one of the persons, at the same moment, we can use the first Thales' Theorem to calculate the height of the inushuk, knowing the height of the person.  

It should be noted that to apply Thales' Theorem, it is necessary to establish the two triangles are similar, that is, that they have the corresponding angles equal or that their sides are proportional to each other.  

Having this established, the theorem is:  

Two triangles are similar when they have equal angles and proportional sides  

In this case of the inukshuk and the person, we have two similar triangles (Figure attached) where $H$ is the height of the inukshuk, $h$ is the height of the person, $A$ is the length of the shadow of the inukshuk and $a$ is the length of the shadow of the person.  

In addition, because both triangles are similar, their angles are similar as well. This means that the relation between two sides of the big triangle is equal to the relation between two sides of the small triangle:  

$\frac{H}{A}=\frac{h}{a}$ (1)

All these lengths can be directly measured, except $H$, which is the value we want to to find.  

So, in order to approach this problem we have to find $H$ from equation (1):  

$H=\frac{A}{a}h$ >>>>This is the height of the Ilanaaq Inukshuk