Stephanie casts a shadow of 1.2 m and she is 1.8 m tall. A wind turbine casts a shadow of 10 m at the same time that Stephanie measured her shadow. Draw a diagram of this situation and then calculate how tall the wind turbine is.
h/10 = 1.8/1.2
To solve this problem, we can set up a proportion between the height of Stephanie and the height of the wind turbine, based on their respective shadow lengths.
First, let's draw a diagram to represent the situation:
Stephanie
/---------------\
/ \
/ \
/__________1.2 m_________\
_
| | \
| ---------------|
| | Wind Turbine
| |
10 m
In the diagram, Stephanie is represented by a vertical line segment, and the wind turbine is represented by another vertical line segment, both with the corresponding shadow lengths labeled.
Now, let's set up the proportion. We can write it as:
Stephanie's height / Stephanie's shadow length = Wind turbine's height / Wind turbine's shadow length
Substituting the given values, we get:
1.8 m / 1.2 m = x / 10 m
To solve for x (which represents the height of the wind turbine), we can cross multiply and then divide.
1.8 m * 10 m = x * 1.2 m
18 m = 1.2x
Dividing both sides by 1.2:
18 m / 1.2 = x
x = 15 m
Therefore, the height of the wind turbine is 15 meters.